The barn I board at isn't really a co-op, but it is kind of similar and I have had shared responsibilities with other boarders at other barns before as well. The most important thing is finding good responsible people with attention to detail. That's also the hardest part
I'd say the second most important thing is to be very clear about what each person's responsibility is.
Here's how it works at my barn:
There are two of us who do most of the care (in a 7 horse barn). I generally come over Monday, Tuesday, Thursday, Friday in the evenings and Saturday in the mornings. The other girl does the same in the mornings, except she takes Sunday instead of Saturday. The BO's take care of everything on Wednesdays and when they aren't out of town, they take weekend evenings. On Weekends that they are away, I do both morning and evenings on Saturdays, the same for the other girl on Sundays and we choose a weekday to take off in exchange. On the rare times that they are gone during the week, they ask one of two other boarders to fill in for $ off their board.
AM chores consist of:
Gather grain dishes from the night before
PM chores consist of:
Turn horses out
Put dinner feed in stalls
Gather grain dishes from the morning
The BO's let the horses in later in the evening and that is the final check for the night. We also have a few weekly chores that we take care of: scrub water buckets, sweep the barn and pick up any manure that has been left on the gravel near the barn.