If you're not going to have anything extending to the ground to support the weight, then you have to find the stud behind the stucco, and mount to that. Not easy to do, but possible.
Do you have access to the other side of that wall? Is it sheetrock? Then you can locate the stud on that side (stud finder, or the "poke a nail" method), and either measure from that to something you can reference on the other side (window, door frame, etc), or drill right through it, sheetrock, stud and right through the stucco, to mark the stud location where the drill bit comes out the other side (you need the right kind of bit for that). If you measure height when you drill that pilot hole, you can use that hole for the first lag bolt. Then use a level to trace the stud for the next hole. Squirt some caulk into each hole before you screw in the lag, to keep the water out.
Fun stuff...