How Many Tigers?

You need another 6 tigers, minimum. With just 6 they will include the rainbows as part of the shoal and nip them just like they do to each other. 12 to 15 is the minimum shoal size for tiger barbs.
Tigers are hierarchical - the nipping is part of the way they sort out and maintain their hierarchy. When tiger barbs are first put in the tank they have to sort out the pecking order, which is why they are particularly nippy for the first few days. If you do get more, they will have to go through the process all over again, so expect more squabbling and nipping.

In theory, all the colour morphs of tiger barb have the same temperament, and they just see other tiger barbs, no colour difference.

Thanks. I'll get another 6 and rehome my rainbows as soon as I can. Having said I can't get a bigger tank, I found myself browsing for 240 litre tanks this morning!

I have a total of 25 tiger barbs, a mix of standard, green, and gold. I don't have anything else in the tank, which is a Fluval Romma 200.
It's the first tank I replanted with @Matt http://scapeeasy.co.uk/advice.htm and this weekend I'll be giving the plants a trim, replacing the moss on one of the caves, and posting some more pics.
Although most of the fish are quite young, when they grow the tank will look full. They are also very active, so I'm happy to have just them in a tank, as there is always enough going on to be entertaining.
I'm tempted to put some nerite snails in with them, as I don't have any nerites in any of my tanks. Perhaps some of the horned ones, to make sure they can defend themselves against any possibility of nipping from the fish.