I'm assuming we basically don't have any art of Gazbaba and Kanisurra, so based on textual evidence, what would be the most authentic way to depict them in art?
Yeah, there are no known depictions of either of them. Due to their relatively minor position we also have no hints like kudurru symbols or astral association to go by (the latter obviously aren’t always indicative of a deity’s iconography, though). Therefore, everything under the cut is, out of necessity, an educated guess at the absolute best.
In theory, one could base their depiction on the famous reference to both of them as “hairdressers of Nanaya”, which lines up with a name of their shrine in Babylon, Eḫilisigga, “house of beautiful adornment”, with ḫili apparently referring to coiffure in this context (Andrew R. George, Four Temple Rituals from Babylon, p. 295). Probably the best way to indicate that would be to depict them with combs or other paraphernalia of that sort. However, Paul-Alain Beaulieu explicitly labels the characterization of the pair as hairdressers as “late theology” (The Pantheon of Uruk in the Neo-Babylonian Period, p. 318). As far as I am aware there’s no strong indication that their character had some intimate connection with hairdressing at any earlier point in time, even though beautician deities do occur here and there (ex. Ninkarnunna in Ninurta’s court). And there’s no shortage of earlier sources associating them with Nanaya - in fact, in love incantations they almost never appear without her (Gioele Zisa, The Loss of Male Sexual Desire in Ancient Mesopotamia. Nīš Libbi Therapies, p. 141; note Kanisurra being invoked with Ishara in a formula on p. 271 though) - so I’m not sure if it would be viable to attribute this to preservation bias. In Gazbaba’s case I’d say we have three different possible additional sources to draw from:
a) the incantation series Šurpu addresses Gazbaba as “the smiling one” (ṣayyaḫatu). I would argue we can effectively treat her expression as an attribute based on that - it is agreed the aforementioned title designates her as a deity linked to sexuality (her very name might be derived from kuzbu, which means something along the lines of “sex appeal”, so i’), since Akkadian love poetry emphasizes smiling quite often (he Loss…, p. 141). Given the fairly stoic expressions of most surviving statues, I think a wide smile would stand out as a unique characteristic.
b) it is possible that Gazbaba’s name was either cross contaminated with Nanaya’s or intentionally modified to resemble it, since the variant Kazbaya is also attested (Jeremiah Peterson, God lists from Old Babylonian Nippur in the University Museum, Philadelphia, p. 71-72). It might very well be just a hypocoristic, to be fair, but given the close association between the two this proposal seems plausible to me. On this basis, I would argue assuming she was also depicted similarly to Nanaya isn’t out of the realm of possibility. Granted, the pre-Seleucid depictions of Nanaya aren’t exactly distinct iconographically, so I’m not really sure if this helps much.
c) the third hint is VERY conjectural, and also only came to my attention so recently I didn’t include it in her wiki article yet: in An = Anum, she occurs on tablet IV, but in a somewhat puzzling position, between a list of steppe-related figures and Ishara’s and Manzat’s mini-sections (Wilfred G. Lambert, Ryan D. Winters, An = Anum and Related Lists, p. 22). It’s an open question if she was listed in Nanaya’s section too, since the latter is poorly preserved; we can only be certain that it encompassed Muati, Kanisurra and Bizilla in addition to Nanaya herself (An = Anum…, p. 177). Why Gazbaba would be separate from her peers is uncertain to me - unless some hitherto unknown characteristic made listing her next to nondescript steppe-related entities or Ishara more sensible to the compilers (granted, there might be no reason, and you could also easily question why is Manzat listed after Ishara and not with other astral deities - my personal guess is that due to both being worshiped on the eastern frontier but this is speculative). I’m not sure if this could translate into any tangible iconography, either - though Ishara does have tons of distinct symbols attested, and the steppe association could lend itself to something like Amurru’s stereotypically “western” iconography, I suppose.
As for Kanisurra: a) the association with love and eroticism, while attested, is not equally strong in her case as in that of Gazbaba (The Loss…, p. 142) - so I don’t think transferring what we know about the latter to her would work. Perhaps building upon the one off Ishara connection - so scorpion motifs of some sort - could work? But I’m not entirely sure if that’s warranted. b) her recurring epithet is “lady of the witches” (bēlet kaššāpāti); there is at least one incantation where the sole difference between copies is that some refer to Kanisurra by name and some simply invoke the bēlet kaššāpāti (The Loss…, p. 430). Per analogy with other more or less positively regarded figures invoked to prevent unwanted interference from beings regarded negatively, one is tempted to ask if perhaps Kanisurra was imagined as a witch par excellence, like how Pazuzu was both the scourge of the lil demons and himself a demonic winged figure, while Ninkilim, the lord of small animals invoked to protect crops from his “subjects”, was seemingly a deified mongoose. Daniel Schwemer appears to more or less go into that direction and notes that “imagery of singing witch-girls that descend from heaven and a young, enchanting and, at the same time, dangerous goddess as lady of the witches illustrates that the stereotype of the kaššāptu has little in common with that of the old hag in European folklore” (Mesopotamia in Guide to the Study of Ancient Magic, p. 52).
If this assumption can be transferred from text to visual arts, perhaps it would be sensible for Kanisurra to be depicted with objects associated with witchcraft; these included just about anything that could be used to bind a person (Mesopotamia, p. 44); figurines or drawings representing people meant to be affected by a curse (ibidem, p. 44-45); water prepared as if it was for funerary offerings for rituals involving the symbolic killing of a person (ibidem, p. 46-47); miscellaneous “sorcererous devices” (upīšū/upšāšû) sent as omens (ibidem, p. 47-48; Schwemer cites an example involving a dead mouse - it required a mouse burial to break the curse). Slander was also associated with casting curses (ibidem, p. 48-49) but I don’t really think there’s an easy way to represent that visually. c) based on the possible derivation of her name from the mythical toponym Ganzer, ie. the entrance of the underworld, and some less certain evidence (presence in mourning rites for Shu-Sin might have more to do with the ceremony taking place in Uruk than with character of any deity involved) it is presumed that Kanissura was an underworld deity (The Pantheon…, p. 316-317).
Frans Wiggermann argues that members of this category were particularly commonly depicted wearing a type of flat cap in place of the usual more conical or cylindrical horned crowns (Nergal B. Archäologisch, p. 224). However, I’m not entirely sure if this is a consensus view; and I’m pretty sure there’s a fair share of depictions of Nanshe where her crown/cap is flat-ish. Still, it’s a pretty distinct article of clothing.
It would perhaps also be tempting to ask if the attendant deities accompany Nanaya in Sogdian art are a distant echo of Gazbaba and Kanisurra - one of the murals from Panjikent shows her with two smaller figures who are “nimbate, with shoulders aflame, carry spears and at least one of them wears armor” (Michael Shenkar, Intangible Spirits and Graven Images: The Iconography of Deities in the Pre-Islamic Iranian World, p. 123; line drawing on p. 307).
The relief from the funerary couch from the Miho Museum also shows Nanaya in the company of two female attendants, though they are not armed, let alone armored. However, while it does appear plausible that Gazbaba and Kanisurra were still worshiped with Nanaya at least in Borsippa and Babylon in the second half of the first millennium BCE (Four Temple…, p. 295-296; note also Usur-amassu with Kanisurra on p. 296), I am not aware of any evidence that they were transferred eastwards alongside her, so I’d be cautious.