It is legal to hunt, shoot and trap coyote's year round. You say residential against woods, is that a large tract of woods or a pocket? The reason I ask is you have to be 300 feet from a residential structure to discharge a firearm on some elses property. If you are in an urban compact Zone than that is out of the question.
If you are not a hunter, find someone in the area that is and give them written permission to stake out the property for the coyote and only that if that is all you are willing to do. There are many people out there that will do this type of thing. Contact your local conservation officer for help or to answer your questions,
http://www.wildlife.state.nh.us/Law_...ment/index.htm , locate your district and call one of the officers on the list and talk to them personally, not dispatch or someone at the answering desk. You can use the exact same coyote call that is in the post above, the whirling thing and that will bring it in on que. Electronic distress calls work even better.
The methods used for shooting would be bow or shotgun (depending on the unit that your property is located in), rifle or as before trapping (the problem with the trapping is that it would be easy for a dog or human to get caught in it if they do not know it is there, that is why all trappers, traps need to be recorded with the local conservation officer as to locate and accompanied with the written land owner permission).
This is for the state of NH, if you are talking about your home in CT, you would need to check with your local CO or the wildlife department in CT on the rules and regs for your particular area.
And yes Canada geese are very tasty, slightly gamier than the duck you would be getting at a local resturant, but very good none the less.
The Canada geese season runs from 9/2/09-9/25/09 this year, go buy a hunting license, a state migratory waterfowl license and go to the post office and get your federal waterfowl stamp and you can harvest up to 5 Canada geese a day with a season maximum of 10, invite some friends over and have a Canada geese party. Then the next season is 10/2/09-11/2/09 and 11/23/09-12/20/09 but the limits reduce to 2 in a day with a max for the season of 4.
Hope that helps