"Sit in a chair" vs. "sit on a chair"

Solution 1:

It depends on the kind of chair. You sit on a dining chair or an office chair, but in an armchair.

Solution 2:

Piggy-backing on Barrie's answer, you could you say that it depends on how relaxed your posture becomes. You sit in furniture where you lounge, and sit on seats where you sit more upright.

So, I'd be more likely to sit on a bench or ottoman, and more likely to recline in a rocker:

It might also depend on the verb you use, too. Consider that blue divan: depending on how much I wanted to relax, I might either sit on it, recline on it, lounge in it, or lie on it...