I just received a reply from my regional CoCoRaHS coordinator:
"Hi Mike -
I believe the CoCoRaHS folks typically use 7am, but they allow flexibility, and 8am reports are frequently used. However, in terms of how we use the data here locally at the NWS Weather Office, as well as the Ohio river forecast center, precipitation data is more tied to GMT (Greenwich Mean Time) - in which we focus on 'hydrologic day.' The Hydrologic day is from 12 GMT to 12 GMT (which, in the summer, is 8am to 8am).
We value your report and certainly will take it if it's at 7am or 8am! If you prefer to send your summer reports at 8am, that still works well for us.
hope this helps - Julie"