But that's not a counter...I absolutely refuse to let luck rule my chances against an Umbreon deck, when I still have to deal more damage to it because of Resistance. I actually found a decent, cheap answer for myself just now.
Lucario UL can 2HKO ANY Umbreon with Bulk Up, short of a belted one with the MD Umbreon on the bench removing its weakness, all at the cost of a single colorless energy. And since straight Umbreon decks have a bunch of holes against anything BUT Vilegar, I expect it to be used more as a tech in SP. In theory, it's a decent 1-1 tech for the Umbreon matchup.
While I'd love to say that Umbreon can be dealt with by a Haunter, that's simply not true. How many KOs can you take before HOPING that the opponent flips a tails on the sleep check just to do a small amount of damage to it? You can only have four Haunters in your deck, and most people only run three.