Front yard or back? You could get fenceposts from a farm & ranch store (there are some that you can "step" into the ground) and wire your trellises to them. If you think that's too ugly (remember that the climbing plants will hide the fenceposts) get stand-alone trellises you can simply push into the ground. If the fence belongs to your neighbor you could possibly be violating the law if you did anything to it or the footings. Instead, make your own.