Every time we've given a tour of our first spawn area, the question always comes up on how we made a rainbow colored beacon.
At first we didn't even know as another player had created the beacon and set the colors, we always just accepted that it was there. It wasn't until enough people asked that we went back to check it out and answer the question.
It is actually really simple; it is just a bunch of glass panes stacked on one another, the light beam hides the glass pane from view so it was hard to tell exactly what was going on until we broke one.
The first pane is a bit tricky to place on the beacon because if you right click the beacon to place the pane, it will open the beacon window. All you have to do is jump then crouch, after that, you just jump and place the pane on the previous one. To make it easy, just place the panes on your hotbar in the order you want so after each placement just scroll to the next one.
Make sure you have an Elytra if you are playing on survival so you can get back down.
This is a great way to have a colorful beacon and not have any of those auto switching Redstone contraptions which, if left in the spawn chunks on a server will eat up resources.
Let us know how this works out for you or if you have any better ideas!