You can normally find your local noise ordinance on your city or county website, if available. If not, the local planning or permits department should be able to get you a copy by fax or mail. Generally in most rural/semi-rural municipalities, it's no 'nuisance noises' between the hours of 10pm and 6 or 7am. This usually includes construction sounds, lawn mowers, dogs barking, and now, I guess, M2s expressing their joy to be outside

In most places, other than between those hours, law enforcement can do nothing unless you are violating another law (as in, if they were breeding peacocks in an area not zoned for livestock). If I were you, I'd get a copy of the local ordinance and read through it throughly. Make sure that the noise ordinance is the only one that was being violated. Then make sure your parents put the birds in the house at 9:45 pm every night (or 15 minutes before the cut-off time).
Most of the places I've had projects in (I'm a civil engineer and did a lot of site planning projects), the law was the noise had to be louder than 60 decibels standing outside of your property line to be considered a nuisance. That's actually pretty loud, and from the way you explain where their neighbors are located, I don't think this will be an issue as long as your parents put them in the house every night. I sure hope that you guys can figure something out with these crappy neighbors. I've had my share of the stubborn ones, so I know what it feels like

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If you do get a copy of the ordinance and don't have a 'legal' friend to look over it, I don't mind giving it a look, if you'd like. I'm not a lawyer or anything like that, but let's just say, it's not the most interesting reading experience

Over the years, I've learned what to look for, so just let me know if I can help