This is by no means an exhaustive list! These are just (some) examples of what offerings I've found to be well received by Thanatos through working with him. Some of these may be UPG.
Plants and Herbs: Calla Lilly, Lily-of-the-Valley, Water Lily, Anemone, Chamomile, Chrysanthemum, Heather, Oleander, Willow, Poppy, Tuberose, Valerian, Wisteria, Crepe Myrtle, Carnation, Holly, Calendula, Mint, Mulberry, Parsley, Thyme, Dragon's Blood, Oregano, Elder, Cypress, Deadnettle.
Food and Drink: Pomegranate (juice, seeds, etc.), Blood Orange, Black Coffee (or tea), Red Wine, Chocolate, Beet Juice
Crystals and Gemstones: Smoky Quartz, Obsidian (black, snowflake, gold sheen), Onyx, Tourmaline, Black Kyanite, Hematite, Scolecite, Bloodstone, Plumite, Jet.
Activities: Lighting Incense, Cleaning (ethically sourced) Bones, Pinning (ethically sourced) Insects, Transitioning, Making Healthy Changes, Reading/Researching Thanatos, Reading/Researching Funerary Rites and Learning How Other Cultures Honor Their Dead, Cleaning Up Graveyards, Death Meditation, Creating and/or Listening to a Themed Playlist (mine is here).
Animals: Butterflies and Moths (if you are pinning dead bugs please ethically source them!), Ethically sourced bones of any kind, Ethically Sourced Feathers (especially dark colored ones), Cicadas and other winged insects (again, cannot stress this enough, please ethically source your dead animals), Replicas and Art of Bones and Butterflies/Moths also work if you don't want actual dead things in your home!
Miscellaneous: Black or Dark Purple Candles, Leather or Earthy Scented Candles, Dead/Dried Plants, Black Silks and Lace, Music.
Most Importantly remember that Thanatos watches over gentle, peaceful death. Anything done with violence, hate, or negativity will dishonor him and may seriously offend him.