How do I hang a round metal art piece on an exterior stucco wall?
This piece of artwork must be between 16 to 24 inches in diameter.  Yes?  Was this originally a barrel stave a ring or a keeper or similar?  They've flattened 3/4 of the band of metal leaving it canted at the bottom, yes?  

I am thinking this is not more than 5 to 7 pounds?  You need to find out the proper weight and then be able to screw a weather resistant hanger into a wooden stud.  Screws, never use nails.  Galvanized hanger and screws or at least powder coated hanger.  Always black color, matt.  

How have your outer walls been constructed?  From the stucco to the interior of your home?  How was your stucco installed?  Is there exterior plywood covered with tyvek or similar?  1/2" to 3/4" thick exterior plywood. I've seen stucco homes built over hay bales and chicken wire. 

In any case, I would use a stud finder and ensure there was a solid 2X4 or 2X6 stud, use a block of wood with cantilevered edges at the top and sides to direct any water away from the stucco, then attach your powder coated hanger hardware that has a short hook or hanger to hold this metal art work away from the stucco but not so much it is able to blow in the wind and move around.  Look for black powder coated hardware. Use pressure treated wood for the blocking and I would paint with black matt exterior coating...if you go that route.

Main thing is to use galvanized SCREWS never nails.  Powder coated hardware.  Screws meant for the weight of this artwork and screwed in to the supporting wall studs or plywood under the siding.

What metal is this artwork?  Is it meant for exterior use to be allowed a natural patina?  I am thinking it might also be best sprayed with a black, matt, Rustoleum spray so it doesn't rust, unless you want rust which looks great.  Make sure the bottom of this piece is secured also so that it doesn't touch the stucco.  If you use a pressure treated block or backing you HAVE to use powder coated hardware as well as screws.  The pressure treatment will dissolve any other hardware within a year.