"If a shotgun isn't an option, rat traps can be baited with suet and nailed to the siding with the set spring in the top position."
Two words: Peanut. Butter. Works on Woodpeckers eating your house, works on rats in the chicken coop and draws just about anything you want to trap and move with a Hav-A-Heart trap. :)
I'd have a hard time killing a Woodpecker, though. I have my "little buddy" that's at the feeder every day for his "suet fix." Luckily, I have aluminum siding on my house. ;)
I love watching woodpeckers, but I've not seen them go for metal. I suppose there's no reason they couldn't