When the panels are assembled the have nails fired into them using a air powered nail gun. My guess is you won't have one of these. Were you to staple it you would need one hell of a stapler. As you can see a a heavy duty stapler will cost more than twice the cost of a new fence panel. You are unlikely to use this tool again.
If you can only access your side of the panel and you don't want to spend too much money.. Looking at the panel go out to the edge where the upright is, that holds the slats in place. Get some 40mm panel pins (£3.99 a at wickes) ..
Lift the slat into place and wedge it there with a screwdriver. Then get a 1.5 mm drill bit and drill a hole through the upright and slat. But only let the drill slightly pierce the upright that will be on the backside of the panel. You now have a pilot hole for the panel pin to be knocked into. Go to the other side of the panel and do the same again. The reason for the pilot hole and the panel pin is.. I know for a fact that your panels will be dried out and brittle. Should you use a thicker nail, you will shatter the uprights when you strike the nail.
Less than a fiver to do the whole thing and you will be left with a box of nearly 200 pins !