The best solution I have seen to this annoying problem when pigeon shooting, is the giant bag made by a friend out of fine meshed net curtain material, complete with drawstring.
He places the pigeons inside, as he shoots them, drawing the neck tight each time.
At the end of the day, all the fly blows are attached to the outside of the bag, and he then simply tips the birds out, and sacks them up in the normal way.
Recently a Sporting Gun reader contacted me to say that he achieves the same result by using a fishing keep net – its green colour also means it can’t be seen by pigeons from the air.
The only other solution is to painstakingly pull the eggs off by hand, not a job to look forward to if you have had a big day pigeon shooting!