There is special food for pups with sensitive stomachs. That may be his only problem and it may not be a long-lasting problem or he may always have a sensitive stomach. Only time will tell.
As far as treats are concerned, Kacee has an iron stomach. I do give her baby carrots as treats, but only one or two, even three at the most in a day. I also give her Bil-Jac liver treats - maybe one or two a day. Once in a while I give her cheerios

. She likes them and that is one thing I used to housebreak her. The other thing I give her is little pieces of cheese

. They all love cheese. I have yet to meet a yorkie that doesn't like cheese, but I'm certain there is probably one or two out there that doesn't.
Try the cheese - just little pieces. Let us know how your little one gets along. How much does he weigh? I love his name, by the way.