Rainbow island doesn't exist.
Yes there is, also known as Floe Island. To get here, you will need the Rainbow pass. Icefall cave also resides on this island, where you have a 1% chance of catching Lapras.
ISLAND 1
The Pokemon day care for Pokemon Leafgreen/Firered is on island 4. You have to beat the elite 4 and get the machine on island 1 working to go there.
You have to get the National dex and Beat the Pokemon league. Then, give the ruby to celio and he will give you a Rainbow Pass. Allowing you to go to the sevii islands. (1 - 7 islands)
The rainbow pass is very helpful because it allows you to go to the islands 1-7.
treasure beach is belw 1 island
Hes bills friend on island 1
Celo, who is in the lab on island 1
He is on 1 island in the Pokemon center building in front of the huge machine
going to the boat in vermillion
on island 1, in the pokecenter. u can get to island 1 by acheiving the rainbow pass
you can rarely find them on 1 island but its easier to evolve a ponyta