Looks like the first turntable was used on Pirana at Efteling in 1983. The first turntable in the US was in 1984; Fury of the Nile at Worlds of Fun and the other two Intiman River Rapids to open that year (Canada's Wonderland and SFGA) also had the turntables. All river rapids by Intamin used turntables until Darian Lake in 1989 opted to go with the belt system for their now defunct Grizzly Run.
In 1988, Hopkins Rides entered the rapids market with Rattlesnake River featuring a single boat length station. In 1990, Holiday World installed Raging Rapids in Boulder Canyon which was made by Hopkins Rides. From videos, this looks to be a straight station but uses the turntable technology compared to the belt system found on the original stations of Intamin. Also in 1990, Frontier City opened their rapids ride, Renegade Rapids which also uses a single boat station with a holding break. Silverwood's Thunder Canyon, manufactured by Hopkins uses a separate load and unload station, separated by a belt lift hill.
The Next Intamin to use a straight station appears to be Kentucky Kingdom's Raging Rapids River Ride built in 1999 followed by Grand Rapids at Michigans Adventure in 2006.
The latest generation of River rapids, Infinity falls at Seaworld Orlando by Intamin and Mystic River Falls at SDC by Ride Engineers Switzerland and Barr engineering have used a continuous moving slatted belt.
TL;DR - Intamin used a straight station using a series of belts prior to 1983/1984 and mostly a turntable station after that.