Any romance manga between a regular guy and idol girl? Where the industry and its people basically try to keep them apart?

REC is about an up-and-coming seiyuu, not an idol, but it's similar in many respects, and their first relationship obstacle is her manager.

REC is a good one, as nacchi mentioned, but you also might want to try Love Lucky. Been years since I read it, but I remember enjoying it, and if I remember correctly it fits what you're looking for.