Well offensively Psychic hits two types SE - Fighting and Poison. Poison isn't that common, and the most common fighting type in OU is Luke, which is hit neutrally.
Defensively you're weak to Ghost, which is quite common; Dark, which means being weak to Pursuit, and Bug, which is less common but there is U-turn around a fair bit.
But I think the problem is more with the Pokemon than the moves. Defensive frailties and poor coverage on a lot of them.
About Jynx, Psychic+Ice isn't great for coverage. You might be better off forgetting the sleep move: it will force a switch to let you Nasty Plot, but given the switch will be to a counter the boost may get wasted. Thunderbolt over Lovely Kiss will get you the unresisted coverage while still retaining dual STAB. Walled by Blissey of course, but that's an issue any special attacker faces. Being weak to Scizor's Bullet Punch is probably a bigger issue.