Membership should be larger than a family but small enough so it would be possible for everyone to know each other personally (even if they may not at any given time). Roughly speaking, the effective community should be within an order of magnitude of Dunbar's number (that is, between 15 and 1500).
Peers should be exchanging or circulating equivalent value among themselves. Beneficial though they may be, a local bookstore or farmer's market is one-to-many and so doesn't count.
It may use a cryptotoken if the token is used primarily in that community and not openly traded outside. It's also possible to choose a peer-to-peer economy that functions alongside a more conventional one, for example a food coop where workers contribute hours in return for membership but can separately use dollars to purchase groceries.
A bowling team or Dungeons & Dragons group without items exchanged doesn't count; neither does a typical chat room. However, a social network with a built-in credibility currency (like subreddit coins) or metric (like Slashdot karma) might.
You can choose an economy you know personally or one you can imagine, as long as it is specific to that place.