You need to call and find a lawyer right away. The first action will probably to get a court order to temporarily block the construction until the case can work through the courts. At the same time, find the list of all your legislative representatives including your senators (you'll have two), your Representative (You'll have one) and your state legislature equivelents (different states use different numbers and names.). Your Rep is your best bet because as of time of writing, it's less than 11 months from election. They can't do much, but all politics is local.
You would also want to start attending local council meetings including school board, meetings of the Parks and Reqs (not the tv show... most counties and cities have one) and find out the name of the organizations that would maintain the park for the public. If the school is a private school, there is still the board of directors and other school governors (I had a similar battle with a private school over similar football related problems for residents. I finally e-mailed the school's president, the dean of students, and CCed the Board of Directors to put them on notice that they were causing real problems and while many of the residents felt the school was quite generous by being open to the public off hours and the last thing we wanted was to resort to legal channels, the issues during home games were frustrating us and we would be holding the school liable for the behavior of students and guests from both the school and the visiting team if the problems continued. It helped immensely if you have an alumn or two (or family of one) who are willing to support... Private Schools bend over backwards if the alums threaten to withhold donations.).
If you're one of those "Football towns" where life revolves around the game, then you might want to organize the neighbors to protest on current game days... see if you can get advance schedule for an organized march on game days on the streets (As I said before, traffic is difficult without streets shut down for protests... try to get the permits for the big ticket games like rivals or schools visiting from out of the area but in your state. Sure your town may hate Shelbyville and their HS football team rivalry with yours is discussed in the most ancient of viking songs about glorious battles, but they hate your team too and are more then willing to support a position against the stadium your town calls home.
As mentioned, check your local ordinances and the zoning for the park space and the stadium. You should also get some info on when the park is opened as they're likely to turn the Friday Night Lights off at a reasonable hour (the aformentioned school had a clock tower that would sound on the hour... but the speakers for the "bell" were programmed to go off at 8 pm at night every night... so it was never an issue with an around the clock chime waking up neighbors at 2 pm.).
These are all constitutional rights under the first amendment, which protects five basic rights, not one (Right to Speech, Right to Religion, Right to Association, Right to Assembly for Redress of Grievences, and Right to Freedom of the Press) and all these rights are on the table and you're permitted a wide breadth of perfectly legal uses of these rights to leverage your governments (You'll have three to complain to. The most local is the easiest to move, but be prepared to take this as high as you can go to get what you want. Don't stop until the Supreme Court refuses to hear your case (or you get lucky and they hear it)... but this is a little below the need to call them in my opinion. Not saying it's not important, just that they have lots of important cases to hear and they aren't young men and women.). Technically, you do not even have to speak to be protected on First Amendment Rights.
One key thing is that unless construction starts to go up, you should only be speaking to lawyers for consultation and to get an idea of local and state laws that the government will be in violation of. The slightly good news is that if you have to go to court, you won't have a jury trial (its good in that you don't have to wait for hours for 12 people to decide... but it's actually more in the states interest than yours. In the U.S. anytime the a government is the defendant in a suit, it's automatically a Bench Trial, which means the judge will also be the jury. The reason for this is that the jury trial is the right of the defense, never the prosecution/plaintiff and Jury duty is never popular... so when the government has to force 12 people to decide if the government was right or wrong over the course of days... well that kinda prejudices the jury... and because Americans have been accused of many things, but placing an overabundance of trust in the government has never been one of them.).
Without your specific state, I cannot begin to find laws (and rarely do I search for specific laws for these answers as I'm not a lawyer... I just have an ability to read the law, attention to details, and a knack for abusing loopholes... finding applicable laws is the dull part of this aspect.). But you should look at zoning ordinances, park ordinances property laws, laws pertaining to large events, and school mission statements (not legally binding, but if you're gonna write a strongly worded letter to any organization, I find that Mission Statements offer enough of a rope in the form of moral platitudes to hang the org over your reverence... and many times, the org ties the noose knot for you.).
