Rather than zapping the pet, give it a good feeling when
inside the zone.
This idea is about a leash that gives the pet a good
feeling, and, using positive rather than negative
reactions, causes the pet to stay inside the premises.
For a short training period you attach the feeling (which
could be a sound or a mechanical patting) with good
reactions from the owner. For example: Each time you
give it some tasty food, or after a game you played with
it, you activate the leash.
Now the leash is set for use. Just like a geo-leash you
the area where the pet is to stay. As it gets close to the
inner "fence", there is a build up of the good feeling. But
it stays or moves towards the outer fance, the feeling
dwindles. As it goes back towards the fance the feeling
gets stronger. Once inside, a "reminder" is given every
once in a while.
Perhaps an "upset" sound can be played, so the pet
that its "loosing" - since it is leaving the area.
I read once that the polar bears in San Diego zoo sit in a
place which is good for the visitors to take pictures,
because they put the air conditioning outlets there...