Four attempts

From what I've read, Georgia has attempted to invade Florida four times.  All attempts failed.

The first one was during the War of Jenkins' Ear.  The Georgians besieged St. Augustine but were forced back.  The Floridians would later return the favor and invade Georgia.  They, too, were turned back at the Battle of Bloody Marsh.  Stalemate.

The other three attempts occurred during the Revolutionary War.  Squabbles relating to military strategy resulted in the duel between McIntosh and Gwinnett.  The war in Georgia was a disorganized mess, though Clarke's victory at Kettle Creek would set the stage for the war's turning point at King's Mountain.

Florida and Georgia would find themselves in opposition again during the War of 1812, but the action there involved federal troops, not Georgia militia, so it wasn't technically Georgia vs. Florida.

Anyway, I find this stuff interesting.