Adaptive Wiener Filter Coefficients Calculation
The Wiener filter is, by definition 

a) not adaptive and 

b) not FIR / AR. 

You seem to want an adaptive FIR filter. 

There are many variants of this: LMS, NLMS, RLS (as you say), or the Kalman filter. Choose your poison! :-) 

ALL of them are (generally) less computationally intensive that the Wiener filter.