One group that could be the kidnappers are AIM (Advanced Idea Mechanics). They're always interested in getting their hands on advanced technology, and Stark has plenty of that. The Ten Rings terrorist organization is also a possibility. They've targeted Stark before and kidnapping him again would be a way to make a big statement. And let's not forget some rogue elements within S.H.I.E.L.D. who might think that Stark is a threat and kidnap him to keep him in check.
In kidnapped Tony Stark fanfiction, villains like Loki could be the kidnappers. He enjoys causing chaos and tormenting the Avengers, and Stark would be a prime target. Another likely candidate is Ultron. Maybe he survived somehow and wants to finish what he started with Stark. And then there are the corporate rivals. Some new, up - and - coming tech moguls who see Stark as an obstacle to their rise and decide to kidnap him to eliminate the competition.