Someone suggested I learn Counter for Blissey, which I didn't even know could learn, but I'm not sure how.
Please specify if it's by egg move, level, breeding, whatever, and thank you.
It is an egg move that happiny can learn. You can breed blissey with Breloom to get counter.
In Pokemon Fire Red, a guy in Celadon City can teach it to one of your Pokemon. This is one way you might be able to do it, but I haven't tried, I'm just guessing and I don't know if the version you are playing is Fire Red. Aside from this, breeding with a Breloom (like PokemonBlack10 said) or another Pokemon possessing the move Counter works for a Happiny inside an egg.