After playing around with /etc/fstab, I came up with these entries for usb sticks.
/dev/disk/by-label/FEDORA /media/FEDORA vfat defaults,user,noauto,noatime,nodiratime,utf8=1 0 0
/dev/disk/by-label/BACKUP /media/BACKUP vfat defaults,user,noauto,noatime,nodiratime,utf8=1 0 0
Apparently, the auto-mounter pays attention to fstab entries. Using /dev/disk/by-label allows the stick to be inserted without worrying about which sd* device it might be. The only caveat is that the mount points must exist before the stick is inserted.
Thanks for the advice SJ.