I've upgraded several databases recently and every time the Database Diagramming feature doesn't work and I get this error: Database Diagram support objects cannot be installed because this database does not have a valid owner blah blah blah.
And every time I've used ALTER AUTHORIZATION command to try and correct the problem (per the message that your receive). While trying to resolve an unrelated issue I stumbled across the EXEC sp_dbcmptlevel procedure. This procedure allows you to set dataase compatibility behaviors from earlier version of SQL Server database. And that did the trick.
EXEC sp_dbcmptlevel 'MyDatabase', '90';
Like magic my Database Diagramming installs and works just fine. For more information you can look at SQL Server documentation here: