Did you go to the add on authors site and see if they upgraded their software?

The add-on author has prepared a new version, so it should be available soon:

https://addons.thunderbird.net/en-US/thunderbird/addon/stationery/reviews/1154701/

(download link has expired)

Phily47 said

I tried to update to Thunderbird 60, but the stationery add-on was no longer compatible. I NEED to use stationery like "Cloud Eight" has made to use with Thunderbird. Now in version 60.2.1, I can no longer use my stationery! I'm reverting back to Thunderbird 52.9.1 for now and will NOT update until the stationery is restored!! Does anybody know if this problem will be fixed soon??

Airmail said

Did you go to the add on authors site and see if they upgraded their software?

Yes, I went to the author's site. The response was: ......................................................................................... by Arivald (Developer) on Aug. 20, 2018 · permalink

Well, new version is ready, but stuck in the review queue. If You want to get it now, You may get the XPI from https://filebin.net/shpxjwfk5mjx63rz and install manually. ........................................................................................ The XPI site listed above does not work. Guess I will have to keep my fingers crossed that a new stationery version will come out soon!