Is there any evidence that Sirius Black mated with other dogs while he was in his animagus form? Assuming that such a thing happened, what would the offspring be? A dog or a human?
There is no evidence that Sirius mated with other dogs while in animagus form. Rowling never wrote anything to suggest he ever did, and we would have no reason to think he would have.
Remember that Sirius only became an Animagus in his fifth year at Hogwarts, and was working with the Order of the Phoenix from immediately after he graduated until when he was locked up in Azkaban. He really didn't have much time to be hanging around as a dog.
Indeed, the only times he seems to have been roaming about as a dog is during the third and fourth book.
It may be worth mentioning that one of the earlier drafts of book four had Sirius staying with other dogs.
When Padfoot returns in 'Goblet of Fire', I initially had him stay with a highly- eccentric, dog-loving old witch on the edge of Hogsmeade. She kept a pack of ill-assorted dogs, was on constant bad terms with her neighbours because of the barking and the mess, and had welcomed in Sirius, assuming him to be a stray.
the old jkrowling.com, Edits - "Mopsy the Dog Lover"
Of course, due to Rowling's highly consistent opinions about keeping sexuality out of the books, it seems unlikely that any bestiality was implied.
As to what form any potential offspring might take on, we don't really know, since such a thing had never been said to have happened in canon. Rowling seems to describe an animagus as having all the natural properties of the animal save intelligence and life expectancy, so I'd guess the offspring would be dogs (if any offspring could/does exist).
An Animagus is a witch or wizard who can transform at will into an animal. While in their animal form, they retain most of their ability to think as a human, their own sense of identity and their memories. They will also retain normal human life expectancy, even if they take their animal form for long periods of time. However, feelings and emotions are simplified and they will have many animal desires, feeding off whatever their animal body craves, rather than demanding human food.
Pottermore - Animagi (behind paywall)