Curse isn't exactly the best thing Umbreon can BP. If this was the case, Umbreon should use a Careful nature, since Defense will already be boosted with Curse. It's also massive Taunt bait, so use Payback over a move.The most important thing here is a Pokemon that can make use of the Curses Umbreon will pass off. Like [supporter]Timbjerr[/supporter] said, Snorlax is a good option; already slow, but bulky with good attack. Other ones to consider are Conkeldurr and maybe Mega Mawile.
Anyway, you also need a poke that covers Umbreon's weaknesses. Aegislash does a good job at that, and even benefits from Umbreon's passes. You'll wanna switch Toxic with Payback on Umbreon. Otherwise it becomes major Taunt and set-up bait. Umbreon shouldn't waste time with status anyway, you need to set up as quickly as possible so it can pass the boosts to something before getting killed.
Sets for each (except Aegislash because that thing has a million sets and I'm not typing them all), if you need 'em:
-Snorlax w/Assault Vest:
Nature: Careful
Ability: Thick Fat
EVs: 252 HP, 252 Sp.Defense, 4 Attack
Moves: Return, Earthquake, Wild Charge, Rock Slide/Pursuit
-Conkledurr w/Assault Vest
Nature: Adamant
Ability: Guts
EVs: 252 Attack, 236 Sp.Defense, 20 HP
Moves: Drain Punch, Mach Punch, Knock Off, Ice Punch (if you can get those last 2, if not go with a Rock attack and Poison jab or something)
-Mega Mawile w/Mawilite
Nature: Adamant
Ability: Huge Power
EVs: 252 HP, 252 Attack, 4 Sp.Defense
Moves: Play Rough, Fire Fang, Sucker Punch, Iron Head/Swords Dance
This is true. A Flying-type works great against both. A good Flying-type to use would be Talonflame. Talonflame is quite common, mainly due to its high Speed stat:A pokemon that is strong against bug and fighting types, as they could cause an Umbreon a lot of trouble wthout any backup.
Talonflame should always use Gale Wings as its ability, as it's the sole reason why it's an OU Pokemon. Flame Body is useless in comparison:This is true. A Flying-type works great against both. A good Flying-type to use would be Talonflame. Talonflame is quite common, mainly due to its high Speed stat:
Talonflame (All-Out Attack)
Adamant
Ability: Flame Body/Gale Wings
252 Speed/252 Atk./4 HP
Item: Life Orb/Leftovers
Flare Blitz
Brave Bird
Protect/Taunt
Tailwind
Tailwind will ensure Talonflame has the upper hand in Speed. Flare Blitz and Brave Bird are very powerful moves, but comes with a high recoil. You can either have it hold the Life Orb for really big power, or Leftovers to compensate for some of the recoil damage. You can either run Protect or Taunt, depending on how offensive you want Talonflame to be. However, a Fire- and Flying-type has a 4x weakness to Rock, which makes Stone Edge a huge kick in the gut. Flame Body has a chance to burn the target. Burn is a good status effect because it lowers Attack. However, Gale Wings is a great ability because it puts the priority of Flying-type moves up.
A personal favorite of mine is Noivern, just because I'm a fan of Dragons. Also, it has great Special Attack and Speed:
Noivern (Special Sweep)
Modest
Ability: Frisk/Infliltrator
252 Speed/252 Sp. Atk./4 Defense
Item: Life Orb/Leftovers
Hurricane
Draco Meteor/Dragon Pulse
Roost
Flamethrower/Focus Blast/Boomburst
Roost replaces lost HP so Noivern can keep on the pain. Hurricane is a very powerful Flying-type move with lower accuracy (70%). This changes under weather conditions: 100% in Rain, 50% in Sun. Draco Meteor is a very powerful Dragon-type move, but lowers Special Attack harshly, so Dragon Pulse is a viable alternative if that is an issue. Flamethrower can cause Burns. Also, I ran Flamethrower when I used Mega Charizard Y in Double battles, where Drought takes effect when you mega evolve it. Focus Blast is a good Fighting-type attack, but at 70% accuracy. Boomburst is a move at a whopping 140 power and 100% accuracy, but as a Normal-type move, doesn't offer a lot of type coverage.
Hope this helped.