First of all, lets eliminate Flareon, Jolteon and Vaporeon since you aready have those 3 types in your team.
So the remaining Eeveelutions are:
Leafeon-Grass.
-Covers for your Flying type's Rock weakness.
-Covers for all of your Fire type's weaknesses.
-Covers for your Electric type's Ground weakness.
Glaceon-Ice.
Covers for your Fire type's Ground weakness.
Covers for your Fighting type's Flying weakness.
Covers for your Electric type's Ground weakness.
Umbreon-Dark.
Covers for your Fighting type's Psychic weakness.
Espeon-Psychic.
Covers for your Normal type's Fighting weakness. (it covers for nothing if Eevee is your Normal type)
I'm guessing the Eevee is the normal.
commented 2 days ago by Scraϝ
So the best Eeveelution for you to have other than Leafeon is Glaceon since it covers for the most weaknesses.