I have just thresholded with the default method of ImageJ the image and set some area constraints to the object to find (i.e. 20-100) with Analyze Particles tool.
Then, supposing that the great majority of the black balls have 3 bright spots I divided the number of ROIs by 3.
I found 373 ROIs /3 = 124 black balls; this number is more or less comparable to the number other has found with other methods.
So now you've a lot of methods and approaches to test.
I compared them to a count of them done by hand (points in green on the below image)
by hand (by my hand ) they are 137.
So it obviously underestimates, but it is not so bad.
As many of us pointed out to you it would be kind by you tell us how much precise you want the estimation of the number of black balls.
But ok, we really don't know if you are still reading us trying to help you;)
have a nice day,