2 glitches that help:

* If mario is riding a visible yoshi, invisible yoshis will not despawn.
* "You can "store" an item swap on an Invisi-Yoshi's tongue by sticking a sprite onto a visible Yoshi's tongue before it's replaced by another Yoshi. When the invisible Yoshi becomes visible again, Yoshi's tongue will spawn with it and grab whatever sprite happens to be in the same slot as the one that you stuck to it before."

Thus:
1. Spawn yoshi 1.
2. Have yoshi lick a sprite. The sprite must be in a lower-numbered sprite slot than yoshi 1. (EDIT: actually apparently not?)
3. While the licked sprite is on yoshi 1's tongue, spawn yoshi 2. Yoshi 2 must be in a lower-numbered sprite slot than yoshi 1. This will cause yoshi 1 to turn invisible, and let go of the sprite. Yoshi 1 still thinks it's licking a sprite, but will store its tongue-out state.
4. Throw yoshi 1 off the edge. (Moving invisible yoshis is only possible for a few frames after mounting.) Before it falls off, get on yoshi 2 so that yoshi 1 doesn't despawn.
5. Throw yoshi 2 off the edge, turning yoshi 1 visible again. It will now resume retracting its tongue.
6. Before yoshi 1 finishes retracting its tongue: load a goal point in the same sprite slot as the sprite yoshi 1 licked, which will warp it down below the level to yoshi 1's tongue. Trigger the tape, which must also be done before yoshi 1 swallows.

I can't think of any to spawn that second yoshi except to get one in your item box from PI.