The ones that V.T.S. & Inland RV sell are 5/32" but you can of course drill out the hole to be 5/32" first. You can get them in 1/8" or 3/16" but I haven't found a source (haven't looked very hard either to be honest).
Put a dab of Vulkem on them as you put them in and twist them around a little once they're in the hole to get a seal all the way around and you'll be set.
For a quick fix until you can get some Olympic rivets, you can get normal 1/8" aluminium pop-rivets at Home Depot (etc) that are easy enough to drill out to replace, and will keep the water out until then.
I've put Olympic rivets in many, many holes in the outside (awning & awning rails mostly) and once they're shaved down and polished a little, you wouldn't even know they weren't there back in 1964