Golf balls in the nest boxes did not work for me when I had a few egg eaters; I had to get wood eggs. You can get them at craft stores (I got some at Jo Ann Fabrics, and ordered more online). I believe one of the only thing that deters them, if you are making "egg bombs" as me and my DH call them, is horseradish.
I also put "curtains" on my nest boxes. I was in a panic to get them stopped, and the curtains look awful...but they did the trick! I set a few egg bombs of horseradish filled eggs, also put a wood egg in each box, and added the curtains. I used an old sheet, nailed it up on the outside of the boxes, across the top, and cut slits in front of each box.
They are most likely lacking in protein; give them meat protein - I believe that helped with my situation as well. I took hot dogs and cut them up and added them to cooked oatmeal....did this each morning for a week, then every other day for a week, then once a week. Throw in a handful of dry cat food as a treat...that's higher in protein, too. Not good to have them on high protein for too long, though.
Also, make sure they have plenty to do! I think that is key. I have a hanging suet feeder that I stuffed FULL of healthy treats such as cabbage and any greens.
Best defense is collecting several times a day. Get the eggs before they can. I did ALL of the above, and my egg eating stopped within a week. GOOD LUCK!