My apologies if I'm misunderstanding the question. My assumption is you are talking about schools that are lucky to have 9 kids on the team. Maybe just to get to 9, some of the few kids that wanted to play went out and recruited their friends who have no experience or desire with regard to baseball. The schools that are lucky to have even 1 coach position paid.
First off, realize that city league schools primarily play other city league schools. So to be successful, here's what you need
Ideally be a teacher at the school so you can recruit kids that will be eligible (or recruit teachers/administrators that can help you with the recruiting)
Good athletes are a plus but not required
You need numbers so you have enough kids as the season wears on and so you can have as big a pool as possible to find the players you need, especially pitching
Also helps if the coach is a teacher that he can stay on top of players that may have eligibility issues
to be a good teacher of baseball fundamentals. Not talking about game strategy or even advanced skills here. Referring to the basics of how to throw, catch, fielding and recording forceouts, catching flyballs, batting (including bunting), baserunning, and, most importantly, basic pitching and catching.
Preferably have, at minimum, 1 very good friend who also is a great teacher of the basics and is willing to help you with practices and games. If you have 2 or more such friends, you are pretty much guaranteed to be wildly successful. These guys should all know how to teach the basics and know drills that will get the players maximum reps performing each of the skills.
Note: I realize that there may be a few super players on these city league teams. The good coach will be able to still be sure they get pushed as much as possible. But the best thing for them on these teams is to develop some supporting players. They have to have someone catch them when they are pitching and to catch their throws when they are throwing to first, etc. Studs are already studs because of athleticism, coaching, or combination of both. You get a lot more bang for the buck by elevating the games of the other players. It's harder to improve the play of the stud. Question: How do you improve on stud going 4-for-4 from the plate? Answer: get some teammates on base and/or get some teammates to drive him in!
In the city leagues I've seen, you really just have to excel in psychology and the ability to teach beginners to pitch. A player that can throw 60'6", has confidence and basic training can be successful at this level. If you are lucky enough to have a few decent arms, those players can dominate at this level with the proper guidance. Given the competition and the level of coaching at the opponent schools, that is enough to win the majority of your games. Basically it's similar to coaching summer youth community teams against other community (non-stacked roster) teams. A coach that can teach at that level can dominate against other coaches that think they know how to play the game but have no idea how to teach and develop players or other coaches that are there simply because they feel it is their obligation.
By the way, if the question was intended to mean what "great" coaches at stacked schools can coach a city league school and still have teams that are as good at the stacked schools, then the answer is that it is not possible for baseball. It's not just the X's and O's, it's the Jimmys and Joes. The gap could be closed a bit if the coach builds the program over several years, but the stacked team isn't competing on a level playing field.