I think you are right that the genie is the only one that produces timeboosters.
But I think that is a good thing. time boosters are just extremely powerful tools and need to be handled with care. Just handing out tons of them for free isn´t desirable (or very likely to happen). So as you suggest buildings like that will have to be limited in one way or another. The genie does it in 3 ways:
1. there only being a small random chance to get any at all
2. by expiring completely after a while
3. By being a very rare and hard to obtain building in the first place
Given all these 3 things it is still an amazing thing to get the time boosters there (the main reason why I place a genie, diamonds being a nice second reason and everything else is just a bonus)
So a building with a 100% chance to make time boosters would have to be much more rare and difficult to get than a genie. That would then be so rare that basically nobody would ever get it at all and what´s the point of that? And what would the occasion be? 19 chests in a tourney sure would be far too easy (we´d get 25 of those buildings every week!) Winning an FA maybe? Happens only once every 6 weeks or so... Could be a very cool prize, but I can already hear the complaints about that....
But if it has to be a 100% chance (I really prefer the lower probability of getting a better prize personally), the production time could be slowed down, to something like say 1 week instead of 1 day. But that is limited by it getting extremely boring to watch lol.
Limiting the expiry date even further? Is a possibilty, but also that has limits or it would be nearly turning the building into an instant to produce another instant... which then is of course rather pointless.
One more possible way to do it is: Make it produce only tiny timeboosts, say 1 min, 2 min, 5 min. that would add a lot of convenience to the game while not actually being enormously powerful in terms of boosting troops with it.
I personally would go for either the small random chance or if people really can´t see any more RNG then I would go for the tiny booster option, at least it would be fun
