I think I personally would have a hard time advertising and "selling" a pet to someone I didn't even know...
...but if I felt like an animal truly wasn't the best fit for our home and family, and that we weren't the best fit for THEM, I would feel good (sad

, but good) about giving them to someone who I knew would meet their needs better. Do you KNOW of an older couple, a handicapped person, or someone else living a lonely and quiet life, who would be blessed by Riley?
Our lab and one of our yorkies were both rehomed to us. Nothing against their former owners, who just lived very busy lifestyles and were never home...but I KNOW that both dogs are living far happier and richer lives now with us. They are both very needy, and needs lots of attention and love, which they get here. The most unselfish and loving thing that their previous owners ever did was recognizing that they weren't meeting their animals needs, and being willing to give them up.
Good luck making a hard decision.