You could probably improve bow technology up to a point - composite bows give you more punch that selfbows and the stiff 'ears' of the Central Asian designs improve leverage in favour of the archer. Not sure whether the compound bow is within the capacity of the Renaissance to design (I suspect not), but it is buildable only in small numbers and at relatively low draw weights.
The problem with rejecting gunpowder, though, is not replacing personal firearms. Many European armies long favoured bows or crossbows over handguns without suffering greatly on the battlefield. The problem is that gunpowder offers a game-changing advantage in the field of siege weaponry. Saying no to it means saying no to mines and cannon, and these are irreplaceable. The only way you couldimagine it would be a deliberate renunciation of a new technology, not exactly something medieval Europe did much. Not without a early and very sifgnificant POD., I'd say.