Dear Kurt Luoto!
Your fink source tree seems to be outdated.
I think, it suffices just to run
sudo fink selfupdate
before trying to install Singular.
sudo fink install singular singular-doc
Looking at this matrix
http://pdb.finkproject.org/pdb/package.php/singularyou can see the current versions of the Singular package in fink and check, that you get the most recent one.
Best regards,
Michael Brickenstein