I am looking to place my 10 year old male that weighs 10 pounds in a loving home that he will stay in forever. Unfortunately I have to give up my own home and move into a rental apartment in the Washington, DC. Tyson was rescued by me 7 years ago, never did I think I need to find another home for him

Tyson is a sweetheart!! He almost never barks, has not bitten anyone ever and is a kissing machine. We haven't quite mastered pad training but his kind heart makes up for that. He can ride in the car with no problem, but usually not more than an hour or so. My daughter is 14 and he grew up with her which was great for the both of them; he adjust to little kids fast. But doesn't like to be picked up by them at all. He won't wiggle or growl, just a miserable look on his face.
Ideally he needs to be in a home where he is the "only child". I have babied him for years so the next home will need to do the same which is why I cannot consider foster homes for him. Tyson likes other Yorkies and some small dogs; but he is scared by big dogs and doesn't take notice of cats.
The separation anxiety is going to be very hard on him. Does anyone have any leads or ideas? I don't want to; but I have a clock I am up against. sigh