Carronades are very straightforward. Their advantages are that they cost half as much to research and half as much to build as other weapon types. This makes them great to increase your Racial Weapon Strength to power up your ground forces if you're going with a missile focussed strategy and need something smaller than an atomic explosion.
They're also suited for jump point defence, where they can negate their main weakness of awful damage drop off. Stations like that would also be good at providing a protection value for the system, both roles where you might not want a missile system.
Plasma Carronades: The best beam weapon in the game for people that don't use beam weapons, since they cover missile's weaknesses at the minimum possible cost.