What can be done to revitalize black slate on an outside porch?

See if this helps!

https://www.msistone.com/blogs/post/2017/03/17/tile-style-easy-care-guide-for-slate-tile-flooring.aspx

https://www.msistone.com/blogs/post/2017/06/30/tips-from-the-trade-how-to-create-a-permanent-wet-look-on-your-slate-floor.aspx

https://www.hunker.com/13420966/how-to-make-slate-tile-shine

http://homeguides.sfgate.com/restore-color-slate-tile-43464.html

Concrete sealer

I would use a masonry sealer.

Try using WD-40 rubbed in in circles..........

You might try a steam cleaning device in a small area. Clean as well as you can, then apply the steam and wipe dry right away with a soft cloth. If the cloth is dirty, then you know that you are "steaming" away even more dirt than was able to be cleaned before. This will be time consuming. After all of the area has been steam cleaned, seal with a good recommended sealer to prevent future damage. Everything I've read suggests sealing needs to be done on at least a yearly basis and probably is necessary for your outdoor porch. Hope you have found the help you need from all the answers provided here.

Best of luck to you.

Clean it with detergent, let it dry and then rub it over with milk! Sue

How to Clean Slate (Homeowner's Guide) - Bob Vila

https://www.bobvila.com/articles/how-to-clean-slate