As far as I know, there is no "easy" software to colorize black and white videos. You can do it, but you have to use your imagination and experience to manually paint in each color to correspond to various shades of gray, and go frame-by-frame. It's a long and painstaking process.
Eventually it may be possible to teach AI to do it, that actually seems like a pretty good use case for machine learning models. But for now you've gotta do it the hard way.
----- Christian Wheel -----
Radio Host, Los Angeles/San Diego/Nationally Syndicated
Audio Production & Imaging
MS Visual Studio Developer
After Effects Enthusiast