When I first put my eBayed Weber DCOE's on my PV they would idle fine, but stumbled badly when the throttle was opened. The problem was that the carbs had dried gummed fuel blocking some of the passages - the accelerator pumps/jets in my case. I had to disassemble the carb completely and carefully clean all the jets and passageways before they started to work like they should.

If you slowly roll on the throttle does it work? Or still stumble? If it runs OK at higher throttle settings then it is probably just the accelerator pump.