Rescuers said Jack and Diane are "very bonded" and it was in the animals' best interest to keep them together.
Carolina Waterfowl Rescue initially thought finding a home for the couple would be difficult, but after their Facebook post about the love affair went viral, they said they received thousands of adoption requests.
In one Facebook post, rescuers said the donkey is protective of the emu and their story is one in which "two creatures with different looks, backgrounds and even breeds learn to stand together, protect each other and love."
Rescuers said that when they tried to separate Jack and Diane, the pair did not get along with other emus or donkeys.
Carolina Waterfowl Rescue officials said they rescued the pair along with several other animals.
The shelter had said the close bond between Jack and Diane would complicate an adoption because rescuers were looking for a permanent home where Jack and Diane could stay together.