Using Centos 7, I managed to install Python 3.6 (https://www.rosehosting.com/blog/how-to-install-python-3-6-4...) quite easily. And of course Python 3.4 is available in the EPEL repo if you need something more "official" (https://fedoraproject.org/wiki/EPEL).
But if you don't want your target machines to install anything, then use nuikta (http://nuitka.net/) on the dev machine to make a stand alone executable out of your python program, and distribute that.
The dev machine needs to be a centos 7 to make sure it will work on the targets (there are other possibilities, but more complicated). Other than that, you won't need to provide anything else. Python will be embedded in the resulting executable, will work transparently, and will not conflict with any existing setup.
As a bonus, the program will run up to 4 times faster, and won't need any admin rights to be installed.
Alternatively, you can use the python-future library (https://python-future.org) to make you program compatible with both python 2 and 3. But it's much more work.