Hi LRM,
The one time we were on the Mariner this past summer, they started taking dinner reservations for alternative dining at 2:30 in the Mariner Lounge, at the entry area by the Compass Rose and Signatures. So I would recommend heading that way around 2:15 to get in line. There was a short line by 2:30 for us.
I don't know when they start taking spa/salon appts. Have a great cruise!
Ginny