For COVID testing in Munich, the least hassle seems to be the Test & Fly center located on level 4 of Terminal 2 at the airport (up escalators from level 3 and go to the far north end of the terminal). 128 euros will get you tested and results set in 3-6 hours, especially if you get there early (they open at 5AM). Testing is quick - I was in and out in less than 3 minutes and they don't flinch when shown a US passport. So quick, terminal parking was 5 euros as well.

You can set appointments - info is here: https://www.munich-airport.com/coron...irport-9526455

Note the there are two types of testing centers on this page, the top one is for citizens, the bottom one "Test & Fly" is for anyone.