I don't think Islam ever had a specific bow...
Are you referring to Arabian bows? Assyrian bows? Turko-Mongol bows? Javanese horn bows?
all these pre-dated Islam
I think, but I think most bows used were of palmwood... it seems the Malay Archipelago picked up firearms pretty early on, but bows and javelins were still used for awhile. Maybe someone else can chime in with more information on specifically "Islamic Malay bows"...
but I was under the impression that the native arsenal perhaps got foreign influence (especially different sword designs) but that the bows themselves didn't drastically change because of Islam...
composite bows which were used in by Middle Eastern, Eastern European, Central Asian, and Indian Muslims didn't seem to be popular in the Malay Archipelago... moisture is high in the tropics and moisture kills composite bows.
Nothing wrong with palmwood longbows. Papuans used longbows too. So did South American natives. The English too used a longbow, but not made of palmwood or tropical hardwood - instead it was yew. African archers such as Hadzas and (maybe the Nubians) which are famed for their archery skill use longbows too.
I HAVE heard of Orang Laut using a pellet bow, which shoots small rocks instead of arrows...