What restrictions are there to building a tower near a private airstrip?
According to this AC you dont need to light the structure, 


  Any temporary or permanent structure, including all appurtenances,
  that exceeds an overall height of 200 feet (61 m) above ground level
  (AGL) or exceeds any obstruction standard contained in 14 CFR Part 77
  should be marked and/or lighted.


But the FAA does have special cases and since you are close to a strip they may require/recommend it, 


  The FAA may also recommend marking and/or lighting a structure that
  does not exceed 200 (61 m) feet AGL or 14 CFR Part 77 standards
  because of its particular location.


Looks like you need some specific stuff to actually light it. Your local FSDO should be able to help out with what ever info you need. As far as I know these kinds of regulations don't change between public and private airports. 

You can find the letter of the law for 14 CFR Part 77 here. The most applicable to your case is quite possibly, 


  (3) A height within a terminal obstacle clearance area, including an
  initial approach segment, a departure area, and a circling approach
  area, which would result in the vertical distance between any point on
  the object and an established minimum instrument flight altitude
  within that area or segment to be less than the required obstacle
  clearance.


Even though you are not directly in line with the runway you may be in conflict with a potential traffic pattern or approach segment.