Since you are in Ontario I will assume you are talking about changing the Ontario regulations.
And they are just "regulations" that would allow night hunting.
Coon hunting at night "with dogs" has been around since before I remember - 40 some years ago I remember hunting coons at night with a couple of beagles. You had to use a 22 and could only shoot them once they were treed (assume its probably close to the same now, haven't done it mega-years now).
That is simply a "regulation" since the hunting laws are pretty broad making it quite a bit easier to change things through a regulation - don't have to convene Queens Park to make changes.
Just like the return of the spring bear hunt and most probably the dropping of Wolf/Coyote tags north of the French/Mattawa rivers, someone (usually MNRF dudes) just has to convince the Minister that there is some need, benefit etc to changing the regulations.
Changes in the regulations are almost NEVER DONE simply to benefit the wants/needs of hunters. You can almost bet the Bear hunt is being re-instated (ok they are calling it a 5 year pilot project) not because of any pressure from "hunters", it's probably more about municipalities over taxing the MNRF with nuisance bear issues AND the whining from all the outfitters, many of them Americans which own camps and pay taxes in Northern Ontario crying because of the drastic hacking of the Moose hunt and the subsequent loss of dollars.
So you would have to convince those that have the ear of the minister that 1) there is a problem that left unchecked is going to cost the government money 2) there is some way the government can get extra revenue "directly" by creating a new regulation 3) there would be absolutely zero flack from the public (unless the cost of not adopting the new regulation would outweigh a bit of bad press that may blow over).
And what I mean is - a recent event in Ontario. A black bear wanders into a fairly dense neighbourhood - numerous people call 911 - the cops come and shoot the bear - there is protests in the streets and an on-line movement to have the officer disciplined, policies changed etc etc.
So while people don't want bears in their backyard, they also don't want them shot.
Now if Coyote's went on a tear and killed every dog and every cat in Vaughan or Kitchener as an example, you might have a slim chance of getting a night time predator hunt approved (no doubt with tons of strings attached), but unless the government can see a political upside and make money in the process, you are probably on an uphill battle that will last longer than your days on the earth.
And if you are just talking about shooting a Yote on your own land because it's a pest, it's threatening your pets or livestock or a coon ripping apart your garbage you CAN shoot those at night under the protection of property regulations - that's NOT HUNTING - and that would be less "ammunition" to support your "want" - they would say "if it's a "problem predator" you can already shoot it at night under existing regulations - no need to have an "open hunt" for them".