Any Water/Ground type with Water Absorb obviously wins so I won't bother posting Quagsire, but I'll add something else to this:
Swampert @ Leftovers
Sassy Nature (+SpD, -Spe)
Torrent
240 HP/52 Def/216 SpD
-Ice Beam
-Earthquake
-Scald
-Stealth Rock
Standard OU defensive set. Here are the calcs for Water Pulse:
4 SpA Jirachi +0 Water Pulse in Rain vs 240/216+ Swampert = 52-62 (12.96 - 15.46%) 9HKO at best
4 SpA Jirachi +1 Water Pulse in Rain vs 240/216+ Swampert = 78-92 (19.45 - 22.94%) possible 6HKO after rocks
4 SpA Jirachi +2 Water Pulse in Rain vs 240/216+ Swampert = 102-122 (25.43 - 30.42%) possible 4HKO after rocks
0 Swampert Earthquake vs 252/0 Jirachi = 236-278 (58.41 - 68.81%) guaranteed 2HKO
So, Jirachi would need to be at +2, with Rain, already have a Sub up, AND use Water Pulse on the switch to even have a POSSIBLE chance to beat Swampert (not even guaranteed). Anything less than that and Swampert owns it without even breaking a sweat. Obviously confusion hax can come into play here, but even then Swampert will almost always win with HP to spare.
There's plenty more too, I'm just getting started :)
EDIT: Figured I'd edit in another counter:
Lanturn @ Leftovers
Volt Absorb
Modest Nature
40 HP/252 SpA/216 SpD
-Rain Dance
-Hydro Pump
-Ice Beam
-Volt Switch
Lanturn walls Jirachi all day, and takes advantage of the rain already being up to pummel it with Hydro Pimp. Here are some calcs going both ways:
4 SpA Jirachi +0 Water Pulse in Rain vs 40/216 Lanturn = 31-37 (7.73 - 9.22%)
4 SpA Jirachi +1 Water Pulse in Rain vs 40/216 Lanturn = 47-55 (11.72 - 13.71%)
4 SpA Jirachi +2 Water Pulse in Rain vs 40/216 Lanturn = 63-74 (15.71 - 18.45%)
4 SpA Jirachi +3 Water Pulse in Rain vs 40/216 Lanturn = 79-93 (19.7 - 23.19%)
252+ SpA Lanturn Hydro Pump in Rain vs 252/0 +0 Jirachi = 225-265 (55.69 - 65.59%)
252+ SpA Lanturn Hydro Pump in Rain vs 252/0 +1 Jirachi = 151-178 (37.37 - 44.05%)
252+ SpA Lanturn Hydro Pump in Rain vs 252/0 +2 Jirachi = 112-133 (27.72 - 32.92%)
252+ SpA Lanturn Hydro Pump in Rain vs 252/0 +3 Jirachi = 91-108 (22.52 - 26.73%)
Even at +3/+3 with a Sub, Jirachi still loses 1 v 1 to Lanturn. I think Lanturn is a hard stop to SubCM Jirachi, because anyone foolish enough to let Jirachi get 4 Calm Mind boosts deserves to lose anyway.