I use Ronseal I think it's called Ronseal garden wood stain. It says on the tin pet safe and plant safe. The great thing about it is it comes in a few different colours. It can be used on planed wood which is good, you don't want to use rough timber of course too sharp.
Can't remember the name of the stain we used not blueberry but summit like that it was a purple-blue colour. Had to restain it and found same brand but in blue in the shed so stained over it with that but wasn't as nice as the purple-blue.
Also stained another one (same brand) with a green colour kind of sage green it's really really nice.
I found a green or light redy brown colour looks really well in the garden but I do like the purpley-blue one as well it's cheery and different.
Have used the stain with no ill effects from any pigs or rabbits, eventhough sometimes parts have been chewed however I would love to get a more natural based one there's an Eco shop that I must visit sometime that stock it.
That could be another option for you is if you have an Eco type shop in your area they might have something you can use that's safe.
Just checking out the Ronseal website they have some of the colours mentioned but I rekon if you go to the hardware store you'll find other colours as well.