Tell firefox to use client certificate for specific site

Question

I am looking for a good way to restrict access to my staging environment without resorting to an ip based firewall.
Basically its a replica of the public production site, that I only want certain people to be able to access. I tried getting this done with http basic auth, but unfortunately, getting this to work with with the api and file subdomain is pretty tedious.

So I was thinking of using https client certificates (which I can send to authorized users) to authenticate and authorize the users on the staging environment. I have created such a client certificate using openssl and I also know how to verify client certificates on nginx. Now I need to be able to tell firefox to only use a specific client certificate on a certain site. But so far I have not been able to figure out how to make firefox use my client certificate on any site.

So basically, how can I make firefox use my client certficate for my stagning environment?