How to correctly fasten a 2x4 spanning garage celing joists?
Assuming you're putting the 2x4 on TOP of the joists, then the fasteners holding it in place are not supporting any load and just serve to keep it from moving around.
I'd just nail or, preferably, screw it in place with some wood screws.
With a 70# load, you're not going to be approaching any limits structurally with a normally built garage but be sure that your pulleys are well secured and the lines are not able to come loose on their own.  A 70# kayak landing on a human is likely to cause injury or death.
I would put the 2x4s ABOVE the joists.  So that will mean getting into the attic above the finished ceiling.  You could attach the 2x4s to the underside but that will be more difficult.  I'd recommend a through bolt (such as a carriage bolt) with washers and nuts.  Something like a 1/2&quot; or 7/16&quot; size.  If you use a screw, I'd use something substantial like:
Structural Screws
Be sure they are long enough to pass through your 2x4, through the drywall and well into the joists.