Holes in offset sistered joists
The rules for notching and boring joists allow you to 


bore holes of diameter up to 1/3 the height of the joist, a minimum of 2" from the top or bottom of the joist 
make notches in the outer thirds of the joist, width of notch up to 1/3 height of joist, height of notch up to 1/6 height of joist  




The question and comments seem to say there is as little as 4" of overlap between the sistered joists, making it impossible to make bored holes that are 2" away from the top and bottom edges of both joists.  

However if a bored hole is less than the 1/6 max height for a notch, it stands to reason  the bored hole can be in that 2" zone;  certainly a bored hole removes less wood than a notch.  

Note that the height of a 2x6 is 5-1/2" and a 7/8" bored hole is less than 1/6th the height of a 2x6.  

Therefore, as long as you 


make holes no larger than 7/8"  (5/8" or 3/4" should be adequate) 
keep them close to the walls / beams, in the outer thirds of the joists 


you satisfy the rules and run your wires without significantly weakening the joists.  I'd aim for the approximate center of the overlap if possible, that should be the strongest spot to drill through.