Having successfully handled loud neighbors who (like yours) were disturbing my son's sleep, I'll share my successful approach and comments.
I think it's better to take it up when it happens if possible, rather than waiting until the next day.
Not wanting to try to raise my voice loud enough to attract their attention, I instead used a very bright flashlight. (This may not work for your exact situation as you say the walls are right up against each other, but more on that later.) Pointing it over the board fence and turning it on and off a couple times invariably got their attention, and then they would stop talking (shouting/laughing/whatever) for a moment.
Having gotten their attention, I could say, without having to shout, "Hey, could you please keep it down?" I didn't have to speak angrily, nor did I want to. They would reply, "Yeah, sorry!" and it would be fine after that (at least for that night).
Repetition had the desired effect. I had to do this several times—they weren't loud every night, but when I first started addressing it they were distractingly loud perhaps once or twice a week. Gradually, this happened less and less often, and then not at all.
The keynotes of my approach were:
Keeping it reasonably polite
(at least, not devolving to angry shouting or swearing—I'm not saying you can't communicate some anger and frustration at being kept up if the situation continues, but hurling insults and just venting will never be productive);
Getting their attention without raising my voice (in my case, by using a bright flashlight) so that my message ("please be quieter") could be delivered calmly, having already gotten their attention;
(In my case, both I and my neighbors have very long driveways, so going up to their door would mean a lot of walking. But if you share a wall that's likely not the case for you.)
Taking it up when it happened, not later.
If you don't have windows and so can't use a flashlight, I would go so far as to go and ring their doorbell and ask them to be quiet. To make it somewhat courteous, you could pay this visit when your son will be going to sleep in about half an hour.
(Loud noises, furniture banging, TV blaring)
Ding dong, ding dong!
(Scuffling, TV stops, someone comes to the door)
"Hi there! I guess you're having a movie night?"
"Yeah, is it too loud?"
"Thanks for asking. Actually, it's been okay up to now, but now my son is getting ready for bed and we'd like him to get to sleep in about half an hour. Do you think you could please turn down the volume, or maybe use headphones?"
If you're friendly in your communication rather than JUST going there to deliver an ultimatum or antagonize him, or vent, or whatever, your communication will reach much much better.
You'll become more real to him. When you're more real to them as a person, when your family is more real to them as a family, they will also be more considerate of you.
After you've had this conversation a couple times, or even during the first conversation, you may also want to mention your son's usual bed time and request that they please keep the volume down after _____ time.
To specifically comment on a couple bits in your description:
I once requested him to please keep the volume down and he did...
This is good news. You're not dealing with just an inconsiderate asshole. :)
...but it is more of a habit I guess because it happens almost everyday.
This is why I recommend taking it up when it happens. After several times of doing that (always politely), they will think, "Let's watch a movie!" and then they'll think, "Oh, let's use headphones or keep the volume down." You could call this "conditioning" but really it's not; it's just being friendly so that your family is more real to them.
I don't feel like complaining to someone everyday about the same thing and appearing whiny...
You won't. As long as you're patient about it and just make the request newly each time. They will probably end up embarrassed more than anything, though that won't be your intention. Just be understanding, and remind them when they need the reminder.
...but then a peaceful sleep for my child is more important to me.
Same here. And they will understand that, also (since it sounds like they're nice people).
They will also appreciate that you're very nice about it (but persistent! Don't be "nice" by never telling them what's happening; that's not nice!) and will respond much better to that friendliness than to expressed annoyance or to "getting them in trouble" with the council.
Good luck! Hope your boy starts getting good sleep and your relationship with your neighbors improves! (And congratulate them on getting married, too!) :)