Try, to measure an existing rivet or drill another out carefully and measure the hole diameter and the required thickness the new rivet/socket is supposed to clinch.
The rivet is semi-hollow so clinch length is from under the bottom of the head to the end. The diameter is rather specific too. Then, search eBay for a vendor. they offer separate listings for each size. if the size is a bit long, plan on using plated washers, these help on wafer sockets to spread the forces of clinching.
https://en.wikipedia.org/wiki/Rivet#Types
https://www.ebay.com/itm/332312242437
That ^ may not be your correct size, it is for my application.
For that size of rivet a setting tool is essential or the mushroom will not form (roll) correctly. I also found these tools online:
https://www.ebay.com/itm/314860296137
That is the tool I purchased for the rivet I got.
The head does require a backup tool, a steel backup block, a brass or aluminum rod will work too. The surface of the backup tool/block must be smooth as any scores or imperfections will be telegraphed onto the head of the rivet, permanently.
If there is a lot of mass for backup it can be hand held, if not, a rod for example, will have to be clamped. Rather awkward for a chassis may need a helper to hold chassis steady. The clinching (setting) tool is not cheap, I paid $55 to set just four rivets but the work looks original. The tool "rests" in my special tool drawer
I did not want to try to set the rivet with a pointed punch or mash it with a hammer
If your not familiar with setting rivets, set some scrap up and practice. Splitting a wafer socket can happen if skill is not there.
I suppose, the setting process could be done in a hand arbor press or a larger (strong) drill press.
You will need a LARGER, ball-peen or smaller sledge with short handle to set the rivet, usually a couple of well placed whacks...
https://en.wikipedia.org/wiki/Ball-peen_hammer
Wear heavy gloves, so if you misfire, the damage is less... Ouch!
Please post results with pix for us all to see.
Best regards
Chas