Large[r] holes (technically, no longer pinholes) need to be patched first with a thin material before painting over. One good material I found suited for this is fabric typewriter ribbon. I don't know if you still have these- those which come in small metal reels and threaded reel to reel across the typewriter's width.
The ribbon is first cleaned of any oily ink. Then cut to a piece large enough to cover the hole. It is then glued over the hole and once the glue sets, is painted over with black fabric paint.
As the others have said, this will only work if the coating on the blinds are still supple. If dried and cracking, other holes will soon form, and therefore curtain replacement is the only feasible solution.