Was it common for ships in the 18th and 19th century to fire at targets along the coast or was there artillery not capable of that sort of indirect fire?

This previous post on AskHistorians with answers by /u/KapitanKurt and /u/mormengilis is somewhat relevant.

You should read that whole thread, but in short: Attack from the sea was relevant enough to result in the building of coastal forts throughout the world. These were effective enough at resisting attack by normal warships to prompt naval powers to create specific shore bombardment vessels. These carried mortars, which would be more effective against fortified positions than the low-angle cannons and carronades carried by normal ships.

I will note further that regular warships could be and were employed (in bombardment and/or with raiding parties) against modestly-fortified positions. The Battle of Grand Port, for instance, saw several examples of this with varying degrees of success.