Retina, 3636 30 bytes
6 bytes saved thanks to Neil
qbnbnrrr /.*bb.(..)*b.*/+V?` Y`rr`rk1`r k Explanation
qbnbnrrr Start with this string Start with the list of pieces except we have three rooks and no king
/.*bb.(..)*b.*/+V?` Keep shuffling it as long as it matches the regex (odd number of pieces between bishops) Y`rr`rk Replace the second r with a Keep shuffling the list as long as it matches the regex b.(..)*b (odd number of pieces between bishops)
1`r k Replace the second rook with a king