Wow, I, uhm, don't know what all to say against Yoshi because there isn't a really good Yoshi anywhere near me. Really, if you don't know how to approach a character, just SHL a bunch until you piss the other person off enough to get him off his game and start making mistakes that you can capitalize on. Remember, if you hit Yoshi off after he's used his second jump, he's done for, but also remember that he's ridiculously heavy during that second jump itself. I don't have enough experience off the top of my head to say whether or not you can spike/Laser Yoshi during his second jump to abuse it entirely, but when he's done with the jump he returns to normal weight, so abuse those two assets then.
Other than that, shine combo/utilt combo if he gets too floaty at higher precentages (not sure) like normal.
Edit: After reading gamer's post which he was writing while I was writing mine, that shine idea is a good one. I think it'd be funny to shine and then JC the shine real quick and spike him to his death too, if you can make it back onto the stage by DIing =P