Hello,
Thank you for using Google groups. I understand you would like to map a custom domain to your App-Engine app.
Based on the documentation provided by Google for mapping custom domains, I believe you have to verify if you are the owner of the domain before you can map it. This is also mentioned by step 2 here[1], where it is advised that only verified domains will be displayed.
It would be my recommendation to try mapping your domain once more by following the guide provided here. Note you can choose the appropriate programming language you are using as well as the App Engine environment.
Hope it helps!