Sorry, I did not get around to trying to repackage 3.7.3 and, since then, 3.7.4 has been released and someone else has now run into this problem on 10.6.  As my Python time is very limited at the moment, rather than trying to find a build solution to make signed flat packages (.pkg) files work on 10.6 again, I have uploaded a copy of the old-style bundle installer disk image file (.dmg) for 3.7.4 which is still produced as an artifact of the build process for our installers so the Python files it installs are identical to those installed by the 10.6 pkg install.  Bundle-format installer packages no longer work on modern versions of macOS but should still be OK for 10.6.  Please test and let me know if it works for you for 10.6 and I'll add it to the 3.7.4 release page.  However, as Ronald noted, be aware that we plan to no longer provide the 10.6 variant installers for Python 3.8.x.

The dmg installer and its PGP signature file are downloadable here:

https://www.python.org/ftp/python/3.7.4/python-3.7.4-macosx10.6.dmg
https://www.python.org/ftp/python/3.7.4/python-3.7.4-macosx10.6.dmg.asc