Residential wiring: round box & outlet?

Round box (4", I think) flush with wall board, used to have lamp fixture attached. Want to install overhead on ceiling one of those "pull it down/push
it back up) adjustable lamps. Lamp cord will run along ceiling and down the wall in plastic Wiremold lamp cord raceway and plug into round box which will contain a single outlet.
I'm having problems finding a way to install a single outlet (duplex outlet is less desireable, but would be acceptable) in the round box, and top it off with a nice plastic finish plate.
I've got everything but the outlet, cover plate, and a means to mount it in the round box. Is any of this possible w/o ripping out the round box and replacing it w/a standard 4-square? (The box is flush with the wall board; no such luck installing a mud ring...)
Thanks,
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DaveC
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DaveC: You should check the bins at your local electrical/hardware store........ a metal cover with a punchout for a standard duplex receptacle is readily available. Most round boxes are 4" ...... however some ceiling light fixture boxes are the smaller 3" variety and will not provide enough room to fit a duplex receptacle......... however there are covers with a single hole to allow the mounting of a single receptacle.... I think that these are for a 4" round box but might be available in the 3" version....... again, check your electrical supply stores or ask an Electrician at an Electrical Contractors place of business.
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Best Regards,
Daniel Sofie
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DaveC wrote:

This does not mean it does not exist - but I've never seen a plastic cover plate that does what you want.
There are metal cover plates that would work. They are round, and allow you to mount a receptacle to the plate, then mount the plate to the box.

You could possibly install an old work box below the round box at the same height as other receptacles in the room, pull romex from the new box location to the existing round box and install your new box with a receptacle there. Add a wall sconce at the existing round box - it'll look better than a receptacle there.
It might be easier and/or better to just install a new circuit (or extend an existing circuit) to a new box in the ceiling. You'll have to decide if that is feasible.

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