Bred by the Dragon - Lyonne Riley

Sammy is on her fifth visit to DreamTogether, a breeding program designed to help monsters create the families they've always wanted. But as hard as she and her dragon partner have tried to create a hatchling, every test turns up negative.

Dragons are dying out, so Zakarion came to DreamTogether to continue his species. But when he can no longer sell priceless artifacts from his hoard to pay for his visits, he takes it as a sign to give up.

But Sammy has grown attached to her dragon, and doesn't want to set aside Zakarion's dream. Perhaps dragons aren't meant to breed in sterile medical rooms, so she offers to continue trying to conceive outside of DreamTogether. Given that dragons live centuries while humans don't, Sammy and Zakarion agree to avoid a romantic entanglement-but as they grow closer and closer, that might just prove impossible.