Thanks for your report. Because of very low usage and the increasing difficulty of supporting new features and bug fixes on very old versions of macOS, like 10.6.x, we no longer provide binary installers on python.org for macOS versions earlier than 10.9. On top of that, there was a specific problem with using the last several 10.6+ installers on 10.6 itself, due to changes in Apple packaging tools. This is the problem you are seeing and was first reported and tracked in Issue36890. As noted there, there is a link to a 3.7.4 installer that will work on macOS 10.6. However, we do not recommend you use it as the most recent release of Python 3.7 is now 3.7.7 with the final bugfix release of 3.7.x coming next month; Python 3.8.3 is now current.

Instead, if you expect to continue using 10.6 Snow Leopard, I would strongly suggest you look at installing Python(s) from the MacPorts project.  They do an excellent job of providing up-to-date versions of open source software, like Python, for multiple versions of macOS, including 10.6. They have pre-built packages of the most recent versions of python37 and python38 for 10.6.  See https://www.macports.org/install.php#installing for a link to their base package installer for 10.6. You can then install Python with:

sudo port selfupdate
sudo port install python37
or
sudo port install python38

Many third-party Python packages have also been ported and pre-built. You can search for them with:

sudo port search py37  # (or py38)

or on their website at https://ports.macports.org

Good luck!