Simple reversible algorithms that satisfies SAC
One simple approach would be, if your input/output size is $n$ bits, is to select a representation of $GF(2^n)$, and a random nonzero value $v$, and have your function be $F(u) = u \times v$ (where $\times$ is multiplication within $GF(2^n)$)


It operates on blocks of fixed size
It is reversible (by multiplying by the value $v^{-1}$)
It satisfies the SAC in this sense: for input bit $i$, and any output bit $j$, flipping bit $i$ of the input will flip bit $j$ of the output for almost exactly half, that is, $2^{n-1}/(2^n-1) \approx 1/2 + 2^{-(n+1)}$


Now, it doesn't satisfy the SAC for a fixed value $v$; for a fixed value, flipping bit $i$ will flip bit $j$ either always or never; so, it might not be the answer you're looking for (on the other hand, it may)