Letisha, I have a riding mower also. And, personally, I haven't had any trouble with running over the nails. I make sure to drop them in the deeper tunnels. When you make the hole in the tunnel or mound, if you immediatelly punch into the tunnel, it is probably too shallow. Most of the nails I've dropped have been 3 inches or more deep. Most of the mounds (where they push up a lot of dirt in one spot) should be several inces deep before reaching the tunnel.
Secondly, if you aren't comfortable using nails, I'm sure any similar object that would fit into the holes should work. I think the main thing is to make it difficult, if not impossible, for the moles to eat and dig their tunnels.