Custom Division with lists - divide by zero

SetAttributes[division, Listable]
division[{1, 2, 0}, {0, 1, 2}]

{-1, 2, 0}

Another possibility is to use Block:

division[a_, b_] := Quiet @ Block[{DirectedInfinity},
    DirectedInfinity[]=-1;
    Divide[a, b]
]

division[{1, 2, 0}, {0, 1, 2}]

{-1, 2, 0}