Hazek, how about this:
A. The private club has a membership fee, and a code of conduct. Send X bitcoins to the club's address to join.
B. Whenever you want to deal with other members under the terms of this code of conduct, use your Bitcoin client to sign a contract (or other document) with the key that was used to pay your membership fee.
C. If there's a dispute, the club adjudicates it. That's what the membership fee is used for. The adjudication process takes account of the club's "code of conduct", and issues a ruling which may include a requirement to make good a failing in a certain way.
D. If a ruling is not carried out, the member is in breach of the code of conduct and can be expelled from the club.
E. An expelled member can apply again by paying a new membership fee. There's no way around this, but they start again from zero reputation, and it gets expensive if they do this too often.
F. Perhaps the members can even choose their own membership fee, since it acts a bit like a security bond. If someone wants to show that they can be trusted, they pay a large membership fee so that others can see that they have a lot to lose if they break the code of conduct.