I read on another post that you are in Fredericksburg. Here are listings of other greyhound adoption groups in the area:
GPA-Richmond (website)
GPA-NoVA (website)
Greyhound Welfare (website)
Greyhound Rescue (website)
Virginia Greyhound Adoption (website)
Without knowing you or your home situation, I cannot guarantee you'll have success with another group. However, different groups do have different requirements. Like others have said, I would contact the group that turned you down for more information.
Good luck!