A Boeing 737-400, EI-CNF, registered to Aer Lingus, and operated by Ryan International Airlines, as a nonscheduled international passenger flight, from Aruba to Cincinnati, Ohio, had a passenger injured during an emergency evacuation after returning to Aruba after departure. Visual meteorological conditions prevailed at the time and an instrument flight rules flight plan was filed. The aircraft received minor damage and the airline transport-rated pilot, first officer, extra pilot, 5 flight attendants, and 148 passengers were not injured. One passenger received serious injuries. The flight had originated from Aruba, the same day, about 1418. The captain reported to the operator that during the takeoff roll, the No. 1 tire failed about 5 knots before V1. He continued the takeoff and left the landing gear down. Ground personnel reported they found tire debris and some metal debris on the runway. He flew by the tower several times and they confirmed the No. 1 tire had failed. They flew around for about 3 hours and burned off fuel. They made an uneventful emergency landing. As planned, after landing, they initiated an emergency evacuation of the aircraft through the right side exits away from the damaged tire and wheel. The right front slide did not deploy properly and they sent the forward passengers through the left front exit.