Can only shoot them at this time of the year if causing serious damage to crops

I'm not certain it's legal to shoot any bird in Ireland with a rifle.

Isn't there conflicting lines on this in the legislation?

Be careful on that one.

Toylexus is on the money as are the other contributors. My addition would be (if possible) to lay out a carcass and get a glass marble (preferably the larger sort (we used call them "golliers" in my youth)) insert marble in the eye socket. All the corvids seem magnetically drawn, as the marble reflects light as would an undisturbed eye and it's the best part, always taken first on a carcass. Best of luck with your endeavours!

You can shoot greycrows the whole year round.

Does the farmer have any barn or out-buildings nearby that you could use as a hide?

You will need to be about 80 yards max. from your bait when shooting with a .22LR.

If no building is available - you need to be well hidden and camouflaged or wear dull, natural colour clothing with a face mask.

Also, keep movement to a minimum….even when well camouflaged they spot movement immediately.

Correct - you cannot use artificial or stuffed decoys..nor can you use a caller.

A dead carcass in a field is not an artificial or stuffed decoy - it's what happens in nature every day.

If some crows are shot - you could prop them up in standing positions to attract others in.

https://www.irishstatutebook.ie/eli/2000/act/38/section/43/enacted/en/html