Guides Dogs for the Blind has a page of information about their “career change” dogs (i.e dogs that are unable to serve as guide dogs).
They say that they have more requests for these dogs than dogs available and that they place pets in homes on certain criteria (not just a simple waiting list). Their website provides information on how you can apply.
They used to have a program for that, but the waiting list became so long that they decided not to continue the practice.