the rental shuttles seem to come by at least every 15 mins. (at least for AVIS). The AVIS store is only about 5 minutes from the ship, so it does not take them that long to make a run. Especially if you are getting off the ship early (because they don't get delayed in packing up people and luggage to go from the AVIS drop off to the ship. We were told the first shuttle arrives about 7:30AM. So if you ask for early disembark, you should be ok.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013