Can it be organised on the day?
To do so, each team must have a spokesperson who speaks for the team. They can use the chat on any server, eg CVS, or the forums, or PMS or SKype, or whatever system they choose, to be able to discuss who plays whom.
To make life easier, in case of any disputes, it may be useful to have an arbiter of some kind. For example, if it is meant to be done randomly, someone has to flick a coin. The arbiter is someone everyone trusts. Who could we pick for that...?
Because there won't be that number of teams, this self-organising should not be that difficult, and is closer to a powerful non-centralised mechanism which could be used in the final CUP competition.
If teams have their own credit system, and there is enough time, teams can organise to play other teams who are available, negotiating which servers they play on. There is no need to determine before hand who is to play who, or who will play who, but a system is required to record results. As teams drop out, so the process of pairing teams becomes more skillful as dgo teams avoid playing each other awaiting their first confrontation to be the final of the entire competition.