I agree with Neil , go to Home Depot (or wherever) and get a 1/16" steel in the Hardware bins .....Remove the post by taking some dykes and cutting thru the rivet as close to the base as you can , otherwise use a dremel or small grinder , do not get it too hot (which is why I suggested the dykes) , then simply push the remaining rivet part into the foam and out of the way ,
You can bend the new piece in the Vice (hopefully you have , or have access to a vice) and you can use a socket to get the rounded bends by placing it in the vice and the metal up against it (the socket laying longways so the part up against the metal is rounded) , use a brass (preferably) hammer and move it accordingly to get the bends in the desired locations (use the broken one as a guide) , then drill the holes for Rivets and the bolt hole , you can reuse the rivet holes if you did not compromise them during removal , (also you can add at least 1 in between the 2 regular locations if you do not use a flanged rivet , preferably in between them and/or in another location to affirm it will hold) , grind or file down the bolt side to taper the end like the original and you are done (do this before fitting it to the seat base) ..... If the rivet locations were compromised then do as Neil said and put them in a different location on the mount , so you have a solid attachment location..... ,
My personal opinion on the Rivets would be to get the ones with Washers (they sell them that way) or the larger flanged head , as you install them from the foam side of the seat pan (you will need to remove the staples from the rear of the cover and lift the foam , or just remove the entire cover and foam to make it easier to work with) *measure how long of Rivets you need , go longer rather than shorter so they hold* , when installing the rivets , place the washer on the foam side of the seat base so it has something solid to suck down to instead of the seat base by itself (or use the larger flanged ones instead) , and it will keep it from compromising the seat base , a cheap electric stapler will reattach the cover , if not Harbor Freight has very cheap Upholstery Air Staplers , you can reattach it , and if you have no use for it again , then just return it and tell them it did not work for your application ... , I guess you could do the same with a Electric one if need be ....
The only other option would be to go on EBay and buy another seat (Used) , as long as the base is good , that is all that matters , as the cover and foam can be swapped from your current one ..... by using a stapler and a flat thin screwdriver to remove the old staples