Celebi is now confirmed to be available in Pokemon Gold/Silver/Crystal! But you have to be willing to risk a few glitches...and you actually need to create a glitch Pokemon through cloning failure.
That's pretty cool. But unfortunately I don't have Pokemon Stadium 2, so I can't risk horrible glitches. But I can always do it on my brother's Silver version then trade the Celebi.
WHAT THE GUY COVERS IN THE VIDEO (Step-by-step instructions):
Be very careful, and don't use a game that isn't your own.
* Beat the Elite 4
* An empty PC box
1. Catch a Sneasel
2. Raise the Sneasel to Lv57. Sneasel learns Beat Up at Lv57. Beat Up must be in the 3rd Move slot.
3. Nickname you Sneasel, "CCCCCELEBI".
4. Make 4 good Sneasel clones
5. Get a bad Sneasel clone (Lv0). This is really hard to do without Pokemon Stadium 2, so just keep on cloning until you get a glitch Lv0 Sneasel.
6. Withdraw the bad clone Sneasel, and give it to the daycare lady.
7. Take the bad clone back. Its sprite in the menu should be messed up.
8. Move the bad clone to the top of your party.
9. Go to your PC, then Move a stupid useless Pokemon to the top of your party.
10. Give the bad clone to the daycare lady. Again. The bad clone should now be in the second slot of your party.
11. Deposit the first Pokemon in your party (The stupid useless Pokemon), and deposite the next 4 Sneasels. If the Sneasels are for some reason now holding mail, remove them all, then deposit them.
12. Take the bad clone Pokemon back from the daycare lady. This will cause your Sneasels to change levels.
13. Give your Sneasels to the daycare lady and take them right back.
14. Now erase your horrible glitch Pokemon. Don't ask how, why don't you just trade your Celebi to a different game then start over.
EDIT: And I just found on Youtube that you can also get a Shiny Mew in the G/S/C games...