There is an awesome set of PowerShell cmdlets out there written by MVP Chrissy LeMaire. This method is my personal choice. It works great and is easy to automate. You can run it with SQLAgent or you can just use Scheduled Tasks in the OS. The scheduled tasks method is a little cleaner, but you don’t get to see it in SQL Server. Also if you are on a cluster and running Windows 2012 you can cluster the task scheduler as an added benefit.
Chrissy wrote this with the intent of making migrations easier, and she succeeded. In fact, I made it a point to thank her at MVP Summit last year because it made my life insanely easier. The advantage here is that you can automate a lot more than than just logins. In fact you can migrate and automate pretty much anything at the server level. Here is the link that I guarantee you are going to bookmark followed by a video demo where I show how to install and automate the syncing of logins using both the SQLAgent method and the Scheduled Tasks method.
DBATools would be my preference in this situation as well, but click through to see four other methods, as well as code.