Do you mean 'service dog' as in the dog would go to a Psych hospital for visits? When I was hospitalized, we had a chocolate Lab that came to visit every Monday afternoon and that was the only thing that would get me out of bed...
As far as a Registry I really don't know....
Our Humane Society has a 'Companion Animal' Program... where we have volunteers take dogs/cats/even rabbits sometimes... to visit the elderly & other places as well (not exactly sure where).. the dogs are temperment tested with our Behaviour Specialist to be sure they are safe/tolerant etc.. So maybe you could see if they have a similar program at your Humane Society
Sorry if this isn't what you meant by 'service dog'...