League of Legends amateur league?
Solution 1:
Every sunday, the ESL organises GO4LOL. If you live in Europe that might be helpful. You could also join the ESL ladders (1v1, 2v2, 5v5). Look it up: http://www.esl.eu/
Solution 2:
If you want to play for fun, I can suggest looking at pages like Battlefy or Razer arena (which was launched just recently).
There you can often find some amateur tournaments for various regions, plus it is really easy for admins to host a tournament.
I don't know in which division you are in, but sometimes there are restricted tournaments as well (e.g. only bronze to platinum allowed), mostly it is up to diamond 1 though.
AFAIK there are some leagues, where you can play in different divisons, according to your skill-level. It is called HouseParty5v5 (and has its own Subreddit btw)
Solution 3:
Short answer: Not official by RIOT.
You can find tons of small tournaments in local areas. Usually made by PC bang or special groups.
Here the Challenger Circuit by RIOT