I posted your request to a dog list I am on. Here is the first response….
The best soft treats are Natural Balance treat rolls - you can get them at any pet store, although I think they're under a different brand name at Petsmart. Basically it looks like a big sausage and you cut it up into small treats.
Be sure to refrigerate it, or it will go bad fast if it's opened and left out. For dogs with sensitive stomachs, the lamb and rice flavor is best (comes also in Beef and Turkey). Also, freeze-dried liver is a good soft treat, although it's a bit rich.
She can also use cut up turkey or chicken hot dogs, string cheese, cut-up boiled chicken, or tuna.