The "Could not verify Recurly's SSL Certificate" error is typically caused by an incorrect subdomain name being entered. When building out your flow you'll likely need to include a host variable. This should be formatted to include only your subdomain, up to the ".recurly.com", not the full domain name.
Recurly_Client::$subdomain = 'mysubdomain.recurly.com';
Recurly_Client::$subdomain = RECURLY_SUBDOMAIN;
Recurly_Client::$subdomain = 'mysubdomain';
Incorrectly configuring you subdomain, can cause errors in subsequent API calls and return the SSL certificate error. If you've updated the formatting and you're still getting errors on, you could attempt to add the host variable using the root path or CACertPath. Specifying the cert path to the certificate on your server could bypass this error. merchant to specify the cert path to the certificate on their server.
Recurly_Client::$CACertPath = 'C:\MAMP\bin\php\php7.2.1\extras\ssl\cacert.pem';
More details on troubleshooting this option can be found here on github.
Finally, if you're attempted each of these troubleshooting options you're still having difficulties the issue could lie in your DNS resolver, preventing your subdomain / host name from being properly applied. In this case you would want to be sure your DNS resolver is updated with the most current version.