Fighting, Bug, and Poison-types all wall and counter Umbreon very well.
Megahorn from Heracross 2HKO's Most Umbreon. (After a Curse, it's a 3HKO)
Close Combat from Lucario 2HKO's. (After a Curse, it's a 3HKO)
Bulky Poisons like Muk can Poison Umbreon, block its Toxic AND Synchronize, and get out-stalled, or force a Baton Pass or switch.