Turk, see if you can visit a good tool store or fastener vendor. They will offer you aluminum or stainless rivets, but probably won''t be able to offer monel - just not enough demand. Stainless is a good choice assuming it''s properly treated before insertion (I recommend Tef-Gel but there are other choices to protect against dissimilar metal corrosion). I''ve mounted much hardware on the last two boats using 1/4" stainless rivets, so 3/16" won''t be a problem for you. You select the rivet by both its diameter and depth, so you''ll need to look at what depth allows you a full pull on the rivet (full distortion on the blind side) before you run out of further pull and the rivet pops. With patience you can also drill out these rivets, but it requires a topnotch metal cutting bit.
Stainless rivets need to be set with a large rivet tool. You may be able to rent one in your area, perhaps from a
rigging shop or a tool rental vendor. Big guns like this (e.g. name brand Big Daddy) are a bit expensive but make a great long-term investment if you plan on owning boats for lots of years.
Jack