Red squirrels could be mass bred in captivity and sold to people wanting them. Whilst they wouldn't be pets as such the squirrels could be semi-dependent on humans by having specially designed feeding stations for them that their "owners" filled. This could provide the squirrels with the edge needed to regain their lost ground.
Similarly, peregrin falcons and sparrow hawks are endangered species and yet cities are full of food. A mass breeding programme could reintroduce these birds to city life bolstering their numbers and reducing the number of flying rats.