Grenade catapults are having a comeback in Syria:
(No photos embedded because Reuters has more
lawyers than me for copyright disputes.)
That's an old idea. Arabs seem to have a weakness for re-enacting the First World War (luckily they don't get the proportions right).
Such grenade catapults are quite cumbersome and thus useful only in rather static tactical situations, a.k.a. trench wars when Europeans do it.
Here's a collection of quick search results showing devices used in 1915 - 1918, when hand grenades were in ample supply and tactical situations mostly static:
video (catapult at 0:33 and later)
a preserved museum piece (17th photo)
Isn't it fascinating how the future of warfare is at times its past, not some hyped gold-plated truck with electronics gadgets that gets ultimately cancelled prior to its production run?
These examples all show Entente devices from the Western front, but that's only because my search keywords were in English. I remember photographic evidence of such devices with German troops as well.
Such catapults are not silent; they can be heard over useful distances at least sometimes. This is the same as with bows, which are not entirely silent either (a concern mostly for aesthetic reasons and for hunting; simple longbows with a feather on the string are quite silent, ancient glued compound recurve bows were rather noisy).
Later on rifle grenades were supposed to replace such devices, and were obviously less cumbersome and thus suitable for more mobile tactical actions as well. Nowadays grenade launcher weapons (oversized pistols) of ~40 mm calibre have largely replaced rifle grenades, but it's no perfect substitute. Rifle grenades keep some of their fascination and utility. Technically speaking, their ability to use fin-stabilised supercalibre projectiles is superior for shaped charge warheads and their fixed weight penalty on the soldier is zero (since they're only munition, requiring no extra weapon unless you want a fancy rifle-mounted sight).