Double sided electrical tape

No friction tape is cloth tape, but only one side is sticky.  I think you're talking about double sided foam tape, I've seen it in black.  It's very soft and indeed sticky on both sides.

I got some black 10 lb 2 sided foam tape from Home depot in the paint department. The interior tape is white, but there is a heavy duty exterior tape which is black.

Eric,

Look for double sided foam tape by 3M. Its black but has a red color backing you peel off. Its heavy duty. Used to be called Body molding tape. It is really strong. They sell it in home depot, Ace, Lowes, etc. 

The same 3M tape is available at auto parts stores - used to hold side moldings on cars.

Scotch 130c linerless rubber.