Okay, so check this out. I've been getting a lot more comfortable with this matchup lately.
I'll admit it; at first, I was highly skeptical of Bringer's dash grab advice. However, I've found that Fox and Falco are complete suckers for Yoshi's dash grab, and it's a great way to break their defense and start a launcher combo. Just thought I'd throw that out there.
Shine combo does hurt. If you can learn to Smash DI it away, you can put your shield up while you're sliding before Fox can upsmash you. I don't recommend CCing the shine unless you're against a wall--you can actually grab Fox out of a waveshine against a wall if you CC it. Eff that JC shine, though. >_> If you DI it behind Fox, there is a very slim chance (this works better if it's led into by the drill) that the shine will actually push you behind Fox thanks to ASDI. I, personally, like DIing away, cuz I can shieldgrab or lightshield the upsmash. DIing back...I'd have to be too ready for it and the upsmash reaches back there, anyway. You could probably pseudo-dodge with a forward smash of your own, but I haven't tried it.
Use neutral kicks (in the air) to combo or trade hits on approach. Use neutral kicks (on the ground) out of wavedashes to approach and interrupt low-flying aerial approaches. Use back aerial to combo...try not to lead in with it too much. If Fox isn't in shield, his upsmash can severely outrange your tail here. If he is in shield, he can just upsmash out of that for a GGNORE.
Try to be a bit more offensive, probably. See which leadins work best for you and try to bait shielding and spot dodges from the opponent...it's a free combo once you can get Fox to make himself vulnerable like that.