TG + RD Manaphy's counters / checks depend on the coverage move its using.
Energy Ball: Tentacruel, M-Venusaur, Amoonguss, Ferrothorn, Celebi, AV Tangrowth, other bulky Grass-types, SpD Dragonite, M-Gyarados, M-Altaria, Kyurem-B, Goodra, (M-)Latias, Dragalge, Empoleon.
Ice Beam: Tentacruel, M-Gyarados, Rotom-W, (M-)Slowbro, Slowking, Manaphy with Energy Ball, Empoleon, Jellicent.
Psychic: Ferrothorn, Celebi, M-Gyarados, (M-)Latias, (M-)Slowbro, Slowking, Empoleon.
Some of those are more viable than others, but all can potentially check or counter it. M-Gyarados stands out as one pokemon that can counter it no matter which coverage move it uses.
As for the CM RD set, counters / checks are most of the pokemon listed above, provided they don't get burned or you let it set up so much that it can break through them. From the pokemon listed above; Amoonguss, AV Tangrowth, M-Altaria, Rotom-W, non CM (M-)Slowbro, and non CM Slowking get screwed over by this set.