Obey or not to obey?

Don't know where you are so the laws may be different but generally it is legal to remove animals that are damaging to property, livestock or crops and / or causing a health menace at any time and in many cases without a license under the land owners instruction.

Thurmond

Check with the game warden first. You can use a for instance question without divulging the land owners name. Specify that it is for crop damage. You may even get a permit in some places.

Believing the "I'll take care of it for you" line leaves you wide open for liability if the guy decides he doesn't want to on that particular day. CYA - Cover Your A$$. 
That being said, T3PRanch and plinker hit the nail on the head, talk to a game warden, check the laws, read the fine print. Don't forget to ask about taking whichever pest animal with a ___ caliber high power AIR rifle. You have to ask the questions that are going to be asked of you when someone sees you shooting animals. Then, get it in writing. 
Once all that is done, shoot me an email. I'll meet you there for some pest control!  

This may not have to be said but, when you head out to take these pest animals keep in mind that you represent all air rifle hunters, pest eradicators, and enthusiasts. We want more farms/ranches open, not closed due to ticked off owners. Bad press spreads so much faster and farther than good press. 
Good luck! I hope it works out for you! 
Tom

I lived and hunted in New Mexico for several years. I suggest that you check the NM game and Fish Proclamation that is available on line I am sure or check with a Game Warden there as the laws are likely more lenient that Texas is now where I currently reside which lets me dispose of the animals I described without license. There are some protected squirrel species in NM and I doubt you can kill anything but collared dove out of season. NEVER take the word of someone else. Check it out yourself and be sure first.

Thurmond

I am surrounded by farms near Syracuse NY, removing nuisance animals on farms happens all the time. Contact your game warden and ask what the law states about nuisance animals on farms. I would not tell the game warden where the farm is. The farmer is trying to make a living.

If given the ok what gun will you be using for the raccoon? I have killed about 8 the last few years they are some tough animals to kill. Check out this video of a raccoon getting hit between the eyes with a 25 cal shooting 47 fpe.

Thurmond is correct about New Mexico. You have to prove that non-evasive doves and birds are indeed causing a loss to the rancher/farmer in question, or you can't take them. If you do take them for damaging crops or feed stores, you must have a license, on season or off season. Weird, but that is the way it is.

The one issue I have, which I wish NMG&F would change, is night hunting. You just cannot under any circumstances. Although I didn't get into trouble, I did have a GW tell me I had to stop shooting prairie dogs after the official sun set time. Nertz!

Always follow your local laws regardless of what the property owner tells you. You should also contact your local Fish and Wildlife (Federal) office as they deal with the animals not covered by Fish and Game (State) if there is issue with a possibly protected non-game species.

Never trust the "I'll take care of it" line. He may think he can talk you out of trouble, but if he's worried about loss of money from crop damages, he'll have a heart attack about poaching fines and replacing your equipment that gets seized.

Lots of good advice here about checking and following laws. I'm a retired FW employee ending up as commissioner officer, wildlife director and ultimately Deputy Commissioner. You would be surprised how FEW bad apples it takes to affect regulations that would hurt lots of honest hunters. If officers reported that air rifle hunters were lawless folk, restrictive regulations could easily follow. I've worked with a lot of terrific, conservation-minded farmers. However, I knew a few who didn't want any wildlife on their property, not even a squirrel eating acorns in the oak trees. 

I would always obey the law, you never know if you are being set-up for a fall. I would not trust that the land owner would come running to your aide if you were arrested. I would either advise the land-owner what you will do for him ahead of time, or wait till he askes why you are not killing the animals that could get you in trouble and then explain your reasons. He may be happy with what you are doing so far that he is OK with you not taking these animals.

Ethics is always a choice. It's what you do when you know you won't get caught that defines character. I personally would rather lose the lease than do things that I know are wrong, even if that law is bogus (like not being able to shoot mourning doves with an airgun)! People may not like you for your "just" character but they will respect you for it.
Hope this helps Mena,

George

Which part of illegal do you not understand? I am insulted that you would even suggest on this forum that the laws are to be disobeyed. An attitude like this serves only to make it difficult for all of us.

Follow the law or prepare to make some lawyer very happy.

Texasleagle, I think he was asking about how to handle the farmer's request and not lose the hunting spot.

Anyone is free to post a question to address an issue pertaining to all things air rifles here. In this case it was hunting with air rifles and which things are allowed in his area. The original poster didn't know if there was a fine line on hunting in season or if an animal is considered a pest destroying crops did the law then not require a permit on private farm land.

In the end he DID check with Game and Fishery and DID ask what to do. That took effort and showed ethical and honest methods of hunting in the future for what state he lives in.

A week later a member here posts a short yet rude comment that we can only gather was directed at the OP. He somehow tried to shame the member for even asking to begin with. Well for all I can tell this issue ended on May 13th when he said he DID check on what was legal and was keeping the thread up-to-date for any that were following.