Can I black list other players?
Is there a way to put someone in a black list, so they can't play with you again ?
In addition to ignoring the person, you could report them for "Unskilled Player". Unskilled player reports never go to the tribunal or result in a ban, but are only used for determining matchmaking [1].
This will not result in a blacklist, but will help to minimize the chance of them being randomly queued with you.
No there is no such thing in league of legends. But there is a report button.