How heavy?

A single molly bolt in 1/2 inch drywall is good for about a 50 pound load.

The molly expands behind the wall as you tighten the screw, then you can loosen the screw to hang the picture as needed (or even remove the screw and put a hook on using the screw to hold it).

If the picture is wide enough you can use two fasteners in two studs and then place the picture as desired (it no longer needs to be centered over the fasteners to hang level).

Well, how heavy is the picture? What are the dimensions? How far are you off in the location in relation to the studs?

I will point out that you will be much better using two hangers rather than one: 1) the weight on each hanger will be half of what it is with one, and 2) it is much easier to hang the picture straight and have it stay that way because it can't swing with two hangers.

In addition, if you use the two hanger approach, you may be able to get it closer to where you want it, AND use one or two studs. I recently hung a large mirror that weighed at least 40-50 pounds. It was about 24" wide: I placed the attachment points on two adjacent studs, 16" apart, and that centered the mirror where I wanted to hang it. Since I used the studs, I didn't need to use bolts or the like: I just used two screws with a washer on each and hooked the wire on behind the washers. If you can't use the studs and have to hang from sheetrock only, then I would suggest you use two moly bolts, or two of those anchors [see link below] that look like a heavily threaded screw: once they are driven in, a screw and washer in each should be fine. The point is that you may have more flexibility and choices if you use two hangers and try to work with the studs.

The two attachment points should be symmetrical with the back of the frame: I usually try to locate these points several inches in from each side of the picture frame, although you can play with this depending on the dimensions. Even if you can only hit one stud, it will ensure that you'll never have to worry about the picture falling off the wall.

So, does that help?

Here is a link that might be useful: Toggler (click on the installation video)

For heavy pictures I use one Hercules Hook and one screw in the nearby stud. Drape the wire over both. See link below for Hercules Hooks info. They really do work nice, used sensibly.

Here is a link that might be useful: Hercules Hooks Tests

Monkey hooks. They are simply amazing. They are cheap at the big box stores but considerably more expensive on line. They are designed to hang on the SR not the studs and require no tools. I've used them for a while now and have never has a single issue and have hung some very large and heavy artwork with them.

I wonder how it turned out.

Anyhow, probably a pair of double or triple nail "ook" hooks would work just fine.