Throw Yoshi over the edge. Yoshi double jumps. You footstool.
Throw Yoshi over the edge. Yoshi tries to do a rising aerial. You dair.
Inhale Yoshi and jump over the edge. Spit Yoshi underneath the stage (works on Dreamland, Smashville, and any stage where Yoshi can't "ride the wall" while still being able to grab the edge).
On any stage where a platform (or you) are being moved (such as Whispy on Dreamland, the moving platform on Smashville) perform upthrow. If you set it up such that you are facing toward centre stage while the landing point gets moved, you land in the air, slightly underneath the stage. Yoshi will get stage spiked. It's hard to explain.
If this is true, then if you inhale Yoshi, and are facing toward the edge, you've already taken the stock. (Yoshi gets timed out eventually, gets auto-removed from Kirby's mouth at a downward angle, and has no means of recovering).