I think most of them say on the tin if they're pet safe.
I've used the Cuprinol Garden Shades (the ones that come in pretty colours) and they're safe but it could work out very expensive to paint the fence with as it's not cheap. :shock:
I did the outside of the buns' kennel with a wood treatment from Wilkinsons (own brand) that has wax added & this helps the water to bead off rather than sit on the wood and soak in. I'm sure Janice from Arc said you can add vegetable oil (I think that's what it was) to normal wood stain for the same effect.