Much more likely would be an extension of the Alloa service to Clackmannan or Kincardine. Since the freight line will be closed, for all intents and purposes, it would be cheap to go and string up some wires and do any necessary upgrade work for passenger operations. Going beyond Kincardine is the problem, as at that point there aren't any towns worthy of a station and it would be faster to drive to Glasgow or park and ride at Inverkeithing for Edinburgh. Paths over the Forth Bridge aren't going to be made available for a Kincardine service, since the entire point of the SAK project was to free up paths for passenger services!
Services that don't go to Glasgow or Edinburgh will always face an uphill struggle in that they will have a difficult time competing with other modes of transport. Frequencies would be low, 1tph at best, which is fine for long distance services to city centres as the added convenience and speed outweighs the longer wait times. That benefit wouldn't really apply on Stirling-Fife services, especially since it's likely that your destination will be some way away from the station. In the end, if TS wants to placate the locals they would be better off phoning up Adrian Shooter and ordering a Class 230 or two to run a wee shuttle service at minimal cost. Anything more than that would be a waste, and exactly the sort of waste that the entire STAG process is designed to prevent. It may well be better to spend money on road or bus improvements than trying to get a passenger service going on the line.