Ok, my trick about playing as a warmonger is to not be even remotely half hearted about it. You need to be decisive and start to utterly crush your enemy quickly, usually right at the beginning of the game. This way you will usually be able to compensate the economic penalty of warring with the spoil of war. In early game, dont hesitate to pillage improvement, raze cities instead of keeping them, so you can keep on destroying the enemy instead of fighting an unhappy conquered populace. Drive your enemy to the edge, then have them pay you tribute in money and techs in exchange of temporary peace. Then go attack another neighbor, repeat cycle, utterly crush everything, burn, loot, pillage, demand tribute. If you are aggressive enough, the wars will pay themselves.
But you also need to have some buddies, use religions to your advantage, your military strength plays in your advantage too. Use your buddies to trade techs and sell resources as much as you can. This will allow you to keep up in tech, until the point where conquest have netted you such a big empire that you will become more advanced and unstoppable, then you can utterly crush them all

Playing this way definitely works at Monarch. So it should do as well at prince.