  We consider generalized $(T, T^{-1})$ transformations such that the base map
satisfies a multiple mixing local limit theorem and anticoncentration large
deviation bounds and in the fiber we have $\mathbb{R}^d$ actions with $d=1$ or
$2$ which are exponentially mixing of all orders. If the skewing cocycle has
zero drift, we show that the ergodic sums satisfy the same limit theorems as
the random walks in random scenery studied by Kesten and Spitzer (1979) and
Bolthausen (1989). The proofs rely on the quenched CLT for the fiber action and
the control of the quenched variance. This paper complements our previous work
where the classical central limit theorem is obtained for a large class of
generalized $(T, T^{-1})$ transformations.
