Want tweak 2 in full detail?
The instant restart method is rule two of this page, expanded into a full page of its own.
Read the instant restart methodYou don't need new games. You need five small changes to the ones you already play.
Most of the football games kids already know, the ones from school, from cousins, from birthday parties, work fine as a starting point. The problem usually isn't the game. It's a handful of habits that quietly turn a fun ten minutes into a game your child starts finding reasons to avoid.

The five tweaks
Nobody goes out. Any game with elimination, "you're out," last one standing, tends to punish the child who's already struggling the most, by giving them the least time playing. Swap it for a version where being "caught" or missing just changes your job for a bit, rather than ending your turn.
Restart in about two seconds. After a miss, collect the ball and go again immediately. Don't stop to explain what went wrong. The pause is what makes a miss feel like a big deal, not the miss itself.
Score effort, not outcome, if you're keeping score at all. A point for a brave attempt lands very differently to a point only for a goal. This one's backed by proper research, not just parenting instinct: children praised for effort and trying tend to stick with things longer after a setback than children praised for the result.
Say what happened, don't grade it. "It went wide" is neutral. "No, not like that" is a verdict. Neutral narration keeps the child's attention on the ball, not on your reaction.
Shrink something. Smaller target, closer distance, softer ball, less space to defend. If a game keeps stalling, the fix is almost always to make one part of it easier, not to explain the rules again.
None of these need any kit you don't already have. They're mostly about what you do and say in the two seconds after something goes wrong, which is honestly the bit most of us get wrong without noticing.

Tweak 3 in action
This is the one that gets the biggest reaction the first time you try it. A shot goes wide, and instead of a small silence you give a genuine thumbs up for the attempt. It feels odd for about two goes. Then it becomes the normal way you play.
Tweak 2 in action
Screenshot the five tweaks above, or bookmark this page, and try applying just one to tomorrow's kickabout before adding a second. Trying all five at once is a good way to forget all five. One at a time sticks.

Why tweak 3 works
This isn't just a nice idea. Research on praise and motivation (Mueller and Dweck, 1998) found that children praised for effort and trying stayed more resilient after a setback than children praised for intelligence or the result, who tended to shy away from harder tasks afterwards. See how Our Kickabout researches its pages.
Keep going
The instant restart method is rule two of this page, expanded into a full page of its own.
Read the instant restart methodWhy elimination games cost the least confident children the most playing time, and three easy swaps.
Read no-elimination gamesSee the three specific games your child probably already knows, fixed with these same tweaks.
Read adapting popular gamesTonight's five minutes
Just one. Add a second only once the first feels automatic.