Hmmmmm, total weight is what, 750lbs? the quietest setup would be the electric hub that MAIN STREET offers for $1k+. of course you can scratch build an electric drive cheaper than what MAIN STREET retails its hub. unsure if 36vdc could pull that rickshaw. a 72vdc hookup probably would.
i presume you're not going faster than 15mph. methinks that a STATON GEAR CHAIN box with HONDA GX50 would fit the bill. the gearbox is made to pull a wheelbarrow full of wet cement, so it's got the low-end torque and it's super-heavy-duty. it'd have to have custom installation, to tie into your main axle.
i wouldn't think of installing friction drive, or anything driving off the wheel(s).
unsure if any gas engine would be too noisy for passengers.