[November 2019]  I needed to install a Python 3.7 environment (env) on my Python 3.8-based Arch Linux system.  Python 3.7 was no longer on the system, so I could not downgrade Python, to install a package that I needed.
Furthermore, I wanted to use that package / Python 3.7 inside a virtual environment (venv).  This is how I did it.
Download Python version source files:
I downloaded the Python 3.7.4 source files from
  https://www.python.org/downloads/source/
to
/mnt/Vancouver/apps/python_versions/src/Python-3.7.4.tgz
I then extracted that archive (source files) to
/mnt/Vancouver/apps/python_versions/src/Python-3.7.4/
Installation:
[Note: in my system env, not a venv.]
cd /mnt/Vancouver/apps/python_versions/src/Python-3.7.4/
time ./configure                 ## 17 sec
time make                        ## 1 min 51 sec
time sudo make install           ## 18 sec
time make clean                  ## 0.3 sec
Examine installed Python versions:
$ which python
/usr/bin/python
$ python --version
Python 3.8.0
$ which python3.7
/usr/local/bin/python3.7
$ python    ## Python 3.8 [system / env]
Python 3.8.0 (default, Oct 23 2019, 18:51:26) 
[GCC 9.2.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>>
$ python3.7    ## newly-installed Python 3.7 package
Python 3.7.4 (default, Nov 20 2019, 11:36:53) 
[GCC 9.2.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import sys
>>> print(sys.version)
3.7.4 (default, Nov 20 2019, 11:36:53) 
[GCC 9.2.0]
>>>
$ python3.7 --version                                                                                                 
Python 3.7.4
How to create a venv for a specific Python version:
  https://docs.python.org/3/tutorial/venv.html
  
  12.2. CREATING VIRTUAL ENVIRONMENTS
  
  The module used to create and manage virtual environments is called venv. venv will usually install the most recent version of Python that you have available. If you have multiple versions of Python on your system, you can select a specific Python version by running python3 or whichever version you want.
  
  To create a virtual environment, decide upon a directory where you want to place it, and run the venv module as a script with the directory path:
  
  
    python3 -m venv tutorial-env
  
  
  This will create the tutorial-env directory if it doesn’t exist, and also create directories inside it containing a copy of the Python interpreter, the standard library, and various supporting files.
    ...
Create Python 3.7 venv [on a Python 3.8 operating env / system]:
python3.7 -m venv ~/venv/py3.7      ## create Python 3.7-based venv
source ~/venv/py3.7/bin/activate    ## activate that venv
deactivate                          ## deactivate that venv (when done, there)
Added to ~/.bashrc:
alias p37='echo "   [Python 3.7 venv (source ~/venv/py3.7/bin/activate)]" && source ~/venv/py3.7/bin/activate'
Test Python 3.7 venv:
$ p37                                                                                                                 
[Python 3.7 venv (source ~/venv/py3.7/bin/activate)]
(py3.7)$ python --version
Python 3.7.4
(py3.7)$ python
Python 3.7.4 (default, Nov 20 2019, 11:36:53) 
[GCC 9.2.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import sys
>>> print(sys.version)
3.7.4 (default, Nov 20 2019, 11:36:53) 
[GCC 9.2.0] 
>>>