Sorry, but as they say, "T'is the nature of the beast"
I only had one cat that was so hopeless at hunting that all he seemed to manage were moths
His brother brought in a blue tit, which we chucked outside. Non hunting brother brought the same bird back in the next day, showing signs of rigor mortis. I think he had happened across it and thought "that's handy, I'll take that in!"
A friend of mine had a cat that was a great one for frogs, she swore blind that it was the same frog that the cat kept bringing in (said she could recognise the expression on it's face
I've been tempted in the past to go for collars with bells, but to be honest I'm more worried about the cat getting caught up in branches etc.
My two cats murder mice, voles, shrews and birds. I believe I posted about finding a dead starling in the kitchen that neither of them seemed to want to take credit for. (Nor did one of next doors cats, Fraidy, who was also present)
At work we now have a "workshop" cat to deal with mice etc, but of course he will no doubt catch the odd bird. I'm afraid it can't be helped.