Google Sites isn't (to my knowledge) set up to use Perl as a back-end service. Read: Google Sites Gadgets, and Developer's Guide (a publication of the API). It appears that Java and Python are supported out of the box.

If you want to do something dynamic with Perl, on the cheap, you can deploy a web application to Heroku, with single-instance apps being free. See Mojolicious::Command::deploy-heroku, for example.

You certainly could link from your Google site to an Heroku app that provides the dynamic content.