Some of my kids were like that, too. Elsa (she's 11 now) was the worst: Her bouncy chair gathered dust because we never used it -- but she did sometimes let us sit. You must be exhausted.
Your son might be the kind of kid who always needs to watch the changing scenery (it's amazing how early personalities can emerge). If so, distraction may help. When you sit down, have toys handy (ones that are easy for him to hold and make fun noises, like rattles or plastic keys), as well as some books (look for board books with pictures of babies). And, of course, try singing songs and gently bouncing him. Hopefully, once he's accepted sitting on your lap, you can ease him into an activity center, where he can stand and bounce and is surrounded by things to play with.
Another reason he may love being carried? The motion itself is soothing to him. If so, a baby swing might help.
The good news is, this is most likely a phase. In the meantime, use a baby carrier of some kind so at least you'll have your hands free while you're holding him.