Formal:
* The quarrelsome nature of the two siblings made it difficult for them to share a room.
* The quarrelsome debate over the new policy left the committee in a stalemate.
Informal:
* My cat is so quarrelsome that he even fights with the plants!
* The kids were being so quarrelsome that their parents had to separate them.
Figurative:
* The quarrelsome wind whipped through the trees, tearing at the leaves.
The best sentence for you will depend on the specific context you need.