Indeed there is.
1. If you want to become a vassal of some king, then you should join battle on his side against their enemies. First you click "quests" on the bottom of the screen. Then you press "factions". Then you click the faction you like and want to improve relation with. Then you can see what other factions they are at war with. Then you go into their territory, and wait for some village farmers. Then you click "We'll see how poor you are after I take what you got". Then your relation with that faction will go down. But you don't have to charge the farmers. You just leave and do this as many times as you want. And you don't have to kill them and feel terrible afterwards. After you have done this, you search for a battle between you favourite faction and the enemy faction. Then you join and when you are done, and you should be victorious, you relation will go up.
2. You can also help caravans that are being attacked by the enemy faction. You must win to get improved relation though.
3. Try doing some quests for the king of your faction.
And, of course, if you want to lower your relation with a faction.
1. Keep saying that you are going to attack village farmers. (Easiest way)
2. Raid caravans.
3. Raid lords parties.
Hope this helps.