There actually is a peace treaty, the 2+4 treaty:

http://en.wikipedia.org/wiki/Treaty_on_the_Final_Settlement_with_Respect_to_Germany

You got me curious, what makes you think that Germany has no constitution?

Not that this is an appropriately cited comment for this sub, but as it's getting voted to hell... Der Vertrag über die abschließende Regelung in Bezug auf Deutschland would be what you're looking for, done in 1990.

As others have pointed out, the "2+4 Treaty" was signed in 1990, declaring "only peace will emanate from German soil" and terminating all "Four-Power" institutions. Accordingly, Germany has full sovereignty, and the US and British forces stationed there are governed by treaties with independent Germany.

Germany does have a constitution, the Basic Law for the Federal Republic of Germany. You might have been mislead by how it doesn't use the word "Constitution," but that's what it is.