In game, you can consult with all your lords before appointing a fief, then appoint the fief to the lord who has the most supporters amongst other lords. This should limit the negative relations hit to the lords who did not support the lord who eventually gets the fief.
Failing that you can modify your game using the module system to lessen the relationships hit. IF you're not familiar with modding the game and the module system this can be a bit of a challenge, but the way to do it is:
Find the file module_scripts.py, and look for the script give_center_to_lord.
Find the line:
(val_clamp, ":relation_with_liege_change", -5, 3)
This line signifies that the relationship change between lords and liege when awarding fiefs varies between -5 and 3. Change those values to whatever you like, for example -1, 20.
Note that this change will also affect other kings, so this makes getting their vassals harder.
To make the change only affect the player, change the line by this piece of code:
(try_begin),
(eq, ":faction_leader", "trp_player"),
(val_clamp, ":relation_with_liege_change", -5, 3), ##CHANGE THIS LINE HOWEVER YOU'D LIKE
(else_try),
(val_clamp, ":relation_with_liege_change", -5, 3), #THIS WILL BE FOR ALL OTHER KINGDOMS
(try_end)
Again, change the values in the above piece of code to whatever you want.
Source: talewords forum.
I don't know about the the diplomacy mod, but the only way I know of to make peace between two members of the same faction is done by talking to your spouse and asking if there's anything to improve your standing in the kingdom. Every once in a while, they'll offer a mission where you can go make peace between two lords in your kingdom (hopefully one of them will be the king).
Another indirect way of improving relations is getting your king to grant that vassal a fief. You can lend your weight behind a lord by talking to them and choosing the option of supporting them in their claim to some fief. If the king does grant them the land I'd imagine that their relationships will improve. Keep in mind, however, that this will alienate the opposing faction. Politics in Caldera is very murky and unsatisfactory.
Best Answer
You can talk to your minister to send an envoy, who's gonna declare a political war on your enemy.
From the inofficial wiki
Sadly, it would still cause problem with your honor rating and lord relations. It only prevents you from losing relationship with city/village/lord you wolud have to harras otherwise.
In order to declare war without consequence, you have to wait for event informing about border incident.