Site with different domain gives cookie login error

So I am trying to set up a new site in my multisite network (running 3.7.1). All plugins are deactivated at the network level. Sites work fine as long as they are subdomains of the original network (testsite.mynetwork.com works as it should).

The problem comes because I have bought a TLD mynewsite.org that I want to be the domain name for another site in my network. I have set up the TLD so it goes to my web host’s nameservers. In my web host’s cpanel I have added the new site as an addon domain, whose document root is the directory (public_html/mynetwork) that contains my WordPress installation (which works fine for the original mynetwork.com site). In the network admin under Edit Site I have changed the domain (under Info) and the Siteurl (under Settings) to mynewsite.org. I It looks fine on the front end; visitors to mynewsite.org see a blank default WordPress page with the title and subtitle of the new site.

The problem is: when I try to go to mynewsite.org/wp-admin, I get a screen that asks me to log in (even though I’m already logged in as the super admin). And when I enter my username and password, I get the warning: “ERROR: Cookies are blocked or not supported by your browser. You must enable cookies to use WordPress.” This isn’t true; I have cookies enabled, and the problem even persists across different browsers.

I presume I need to configure something differently, but what?