The obligation to ruff in coinche
Usually yes: if you can't follow the led suit, you must ruff (play trump), with some exceptions.
The basic rule
When a suit you don't hold is led, the classic coinche rule forces you to ruff, that is, to play a trump and try to win the trick. You can't freely discard another suit as long as you still hold at least one trump.
The partner-is-master exception
The main exception (widespread but still a convention): if your partner already wins the trick, you don't have to ruff. You can discard safely, since the trick is already going to your team. Do check that this rule is accepted at your table.
What if someone has already ruffed?
If an opponent ruffed before you and you can't follow, you should in principle overruff (play a higher trump) if you can, otherwise you still play a trump. Again, the duty to overruff depends on the conventions: some tables don't enforce it. With no trump at all, you discard.
See also
FAQ
Must you ruff when you can't follow suit?
Usually yes: without the led suit you must play a trump. The main exception, by convention, is when your partner already wins the trick.
Can you discard instead of ruffing?
Only if you have no trump left, or, depending on the table convention, if your partner already wins the trick. Otherwise you must ruff.