Gunpowder is a spectrum; that is, there are many many variations on gunpowder.
Zinc-sulfur would be one alternative, though I doubt it would be "weaker" than gunpowder -- have you ever seen video of an actual zinc-sulfur rocket, compared to a black powder engine (like Estes model rocket motors)? Zinc-sulfur is actually closer to flash powder (metal as the fuel, mixed with an oxidizer -- in this case, sulfur -- but not intimately incorporated like good gunpowder), and any form of flash powder is very, very hazardous to use in a metallic confinement like a gun barrel -- confinement can cause pressures to spike far beyond even smokeless powder's normal operating ranges.
However, gunpowder itself ranges from "pretty bad, hard to ignite, slow burning" for primitive forms (just mixed powders) to "top notch" for commercially produced (and some homemade) versions, easy to ignite, fast enough to make good firecrackers -- even with the same formula. Add in variations of formula (extra sulfur to produce more smoke also make the powder slower and weaker, for instance) and there's a broad range of "gunpowder". If the makers are new to the trade, they may not yet have arrived at an optimum mixture, or (due to things like quality of the available charcoal, perhaps not completely in their control) even the optimum mixture they can make is not the best that could be made with the best ingredients -- just as 14th century gunpowder couldn't hold a candle to 18th and 19th century products.