well if you can catch them, maybe trespass. A better solution would be to put down a LOT of pepper dust ot a gel stuff called Get off my garden. This will deter the dog from wanting to go there.
I think you will find that trespass is a civil offence and would require a court order to prevent this person from allowing their dog to foul your garden. What I would do is to set a video camera or take photos and maybe show them to the person concerned or to the dog warden.if you witness it happening you could go out with a poo bag, pick it up and ask the person to take it with them, this would be especially effective if its a busy neighbourhood and you created a bit of a scene.
I have 2 Irish Wolfhounds and when they poo you almost need a wheel barrow to remove it, but it always gets removed, if I left it, everybody would know where it came from, their poos are bigger than most of the dogs around here :)
Ring the council - my neice had this problem, they provided a sign reminding that dog fouling is subject to a fine of £50. However, you still have to catch 'em, and if it is a lone dog then you have to make it an uncomfortable place to poo. Holly is good! - seriously though, Homebase do a very smelly gel granule (called something like Dog Poo Off), you sprinkle it and the dog won't go near. (Sorry to say, nor will anyone else for a few hours, it's very ammonia-y!)
Boxtops, only £50.00!!! they put a sign up in my road stating the fine was £2.000 I should keep that quiet or you will have all the dogs in my area crapping in your nieces road!! :)
I was going to suggest video or photo as well
I find this sort of thing disgusting - but remember it's not the dogs fault.
have you confronted the dog owner? What did they say if you have? Do you know who's dog it is? Follow the dog home to find out