Bill is right about replacing if you can - you might try Gorilla Glue - available at most Home Depots and Menards.  Very good stuff - follow the directions and don't get it on your hands.  It will bond just about anything to anything.

http://www.gorillaglue.com/home.htm

I know the question was about glue to attach a new rubber cover to an old running board. Having been there, done that, I will offer the  folllowing info, the reader can decide what works best for them.

I talked to a lot of people regarding the pro's/con's of recovering running boards and with out exception I found the common oppion to be that recovered boards were nothing but a big problem. On the advise of several people I purchased new boards from Buckeye Rubber. Buckeye's boards resemble the original boards very closely, the fit was perfect and I did not have to go through all the prep work required to recover old metal that has out lived it's usefulness....Bill

the newer polyurethane glues will bond steel and rubber.  Since they expand as they harden they fill gaps where water may seep in.  I would try it on some trial strips until u figure out how to deal with the over expansion as it squeezes a foam like hardened glue out where u put a bit too much, and it needs to be cut away.  I have used it in my woodworking shop for outdoor things like birdhouses etc.

I recently replaced the running board rubber on my 1939 Plymouth Deluxe but the glue I purchased is not boading to the running board well.  Is there a product that I can purchase that will bond to rubber to the board? Where can I purchase it?