Due to how little DC publishes Wonder Woman and or Wonderfamily stories, her cast isn’t as big as Batman or Superman’s, so I wouldn’t say there’s a ready-made Wonder Woman character to slot in that spot.
Pairs, in this case a wonder-bat pair, are typically designated by relationships, being created in the same era, and/or being the same age, and there really isn’t someone who ticks all the boxes for Duke to my knowledge. Especially era-wise, the new52, while great for Duke, was kind of a dark age for WW, so it never created any heroes with staying power in her corner of the universe. But there are some other characters who could fill that role which I'll discuss below. This is really just an excuse to talk about WW characters for me, so… sorry for the length 😅 (And since I mostly know WW stories from post-crisis, that will probably show in how much I can say about each. The post-rebirth characters I really only know though the fandom wiki and some light skimming of their comics.)
1. Olivia Desmond (Nightbuster)
This is what I think you’re looking for most. Daughter of Blockbuster and Jezebel Jet, she’s a huge Nightwing fan. She was saved by him and the Titans, and given sanctuary in Themyscira by Donna Troy. She has inherited super-strength and presumably in the future, Amazon training. Like Gotham Girl, she’s Batfam-adjacent already, and with these three you can create the New Jersey Justice League! There is the small caveat of her being 9 years old as of her last comic, but it’s been three years and no one’s done anything with her. We could easily fudge the numbers of her aging or just throw her into another dimension to age her up some. (And just look at her, what a cutie <3)
2. Maggie (of the District of Columbia)
A normal waitress from Washington DC entrusted the sword of Antiope, who earns her place with the Amazons of Themyscira. She’s got a magic sword that gives her battle prowess and flight, plus Amazon training. Young adult-aged, with pretty much no backstory to my knowledge, despite being in over 20 issues of WW (not even a last name…). But I think there’s something to both her and Duke having originated from a working-class, relatively normal existence, and getting thrown into this crazy fantastical world of gods and superheroes and princesses and billionaires. She’s got potential, and at the least would make for a good liaison to Duke in a Themyscira-related plot.
Daughter of Circe and Ares, she was taken from Circe’s care by the Amazons and raised as one of their own, only to be kidnapped by Ares (and that plot thread has been left hanging for 20 irl years…). She has both magical abilities and Amazon training. As mentioned, it has been so long since she was last seen as a child/pre-teen, she could be reintroduced at literally any age and it would be fine. She could have interesting stories with Duke around villain parents (Circe-Gnomon teamup?), and their complex relationships with their saviors (the morality of the Amazons taking a daughter away from her mother is ambiguous, and while Batman didn’t do anything as bad, Duke definitely has complicated feelings about it all).
Wonder Boy! Okay this is actually just a normal boy. He doesn’t have powers or anything, but he’s the nephew of a UN ambassador who briefly dated Diana. She named him Wonder Boy in a cute comic of him getting to join her on a day in her life as Wonder Woman. We haven’t seen him for a while, and in fact, since last we saw him, his uncle died heroically helping Diana! We just never got that followed up from Bobby’s perspective. He and Duke could bond over the grief they have over loved ones, and really it would just be nice to see Duke in the Barnes’ home, spending time around a Black family in a way he hasn’t really gotten to since his parents. Plus, it’d be interesting if he worked in youth outreach, similar to what he watched Diana do on their day out. Then they could make a connection through the similarities of that and the WAR movement. And like, we’re talking about a team-up with the Bats here, almost all non-powered. Bobby could have easily taken some fighting lessons in the 20 years since he was in comics if we need them to fight bad guys together.
Even though Wonder Woman doesn’t have the most robust cast, all of these characters have a lot of potential in the stories they could tell, and I’d enjoy a team up between Duke and any one of them (or really between Duke and anyone. please dc im begging). Hope this satisfied your curiosity!