I had that problem too
My 88 had a spark problem. I threw parts at it. It was not the CDI black box, it was the stator (behind the flywheel).
Other tips.
1) Sand all gound points, where the coil mounts, the engine mounts, any contact points for ground.
2) check the spark plug boot, they can get loose and need replacing
3) fresh plugs, have several on hand
4) get clear fuel line, it is nice to be able to visually see if fuel is getting to the carb - I was having problems with fuel at the same time, that only confusues things, believe me.
5) You can get a new stator for around $40 from Ricky Stator dot com
6) It is very difficult to verify with a test meter is a CDI box is good or bad, best to get a used one from somewhere and test it that way
7) My spark tester shows a "weak" spark, but it starts every time now that I have the new stator, new plug, and fuel issues sorted out.
You can read about my saga in another thread if you like...
Click Here - 88 KDX no spark