"The contingent spell takes effect only on you, even if it can normally target others"

I don't think the spell being intended to affect others is a problem here.

I don't think there is any issue with a contingency being on knockout. It seems like a perfectly reasonable and intended trigger.

What is more of an issue is that the spell does require an attack roll. There is no RAW mechanic for allowing a hit, so I think to hit yourself you do have to successfully roll to hit. Knocked out means that a player is unaware of its surroundings, can't move, and is incapacitated. I think even though the spell could otherwise trigger, the character doesn't have the ability to compete the requirements needed at "spell engagement", more on this later. Under this reading a DM could still allow it via rule of cool, but keep it mainly grounded with a con save to allow the attack and/or use disadvantage on the attack roll.

There is another way to read this, as contingency that says the spell is cast ahead of time, but doesn't go into affect until the trigger. Above I had to use the words "spell engagement", which I pulled out of my ass to say when the trigger went off. It could be argued that the attack is actually part of the spell casting. If so then the attack roll on themselves would occur before the knockout and that could let it work. Then the only question is does the damage occur up front or at trigger. I'd argue that if damage occured up front it's a little more balanced, however if the trigger was if something like "immediately before I'm knocked out" (which I personally might require a check at casting for that kind of accuracy) I might let them keep the concentration on the spell as they take no damage and were never truly knocked out. If they take damage at trigger instead, then they were definitely knocked out, and if they were knocked before they were healed the spell went into affect when they couldn't hold it up with concentration as they were out, so the spell is just one time healing, if valid at all as they were never able to concentrate.

Either way, this is not really op rule gaming, despite all the chicanery and hoop jumping. Contingency is sixth level and could work with a normal healing spell if they had one. It's also very likely to not be huge in a fight with the best case being that it was prepared by a very high level wizard who long rested previous to battle. The minimal version requires level 11 wizard who is knocked out and comes back with an average of 10 HP (unless upcasting vampiric touch) and it's not even their turn. The most op version for a level 20 wizard using a ninth level upcast of vampiric touch still only averages 31 HP. They stand a good chance to be hit by a second attack and downed again with the CR of creature they are likely fighting at these levels, and this trick is only really decent once a battle.

I also added a version of the goose into our campaign. It followed essentially the rules here and appeared in a level of the Dungeon of the Made Mage. I also gave it a "honk" action as an AoE that would require a constitution save or on fail would cause the affected creatures to stand up, drop whatever they were holding, and cover their ears, becoming restrained until the start of the gooses next turn. I think I had also given the goose a fairly weak peck attack and disengage as a bonus action.

The players would bump into the goose in heavily trapped areas, with traps that by themselves were relatively innocent. A series of chains hanging from the ceiling, but not quite touching the floor that when disturbed shot arrows at chest level towards the disturbed chain. A long hallway of difficult to spot pressure plates, that would trigger blades to swipe at anyone on the pressure plate. That kind of thing. I also created a network of goose sized twisty turvy caverns for the goose to easily navigate from trap to trap without allowing an easy line of sight for long. If the players followed through the caverns they'd be on difficult terrain leaving the goose an opportunity to break line of sight, lose them in the maze, and potentially split up the group.

You can imagine the players on their bellies sliding underneath the chains, when out of a hole a goose waddles out. The players pleading with it to be a good goose when HONK half the players standup bumping into the chain and getting shot by arrows. The goose navigating nonplused back into the small acid etched cavern with players reluctant to follow. Then there's the goose, at the end of the next hall! The players running after it as pressure plates trigger, some having the common sense to stop and take their time, others rushing with wanton abandon. The goose disappearing into another tunnel where one or two give chase losing each other and their way in the maze. The goose appears from around a cavern corner to peck a slow moving character in the face for one or two damage and disappear around the corner again.

It was one of my favorite campaign moments.