This sounds like a great application for a bail with a tube rivet!
It depends on the hole size with which the heart is drilled, of
course, but it would be a relatively gentle cold-connected bail that
would look very nice.
The bail can be made from a bit of half-round wire, or you can forge
flat the ends of round wire if there’s none handy. Drill holes in the
ends a bit bigger than your tubing, and bend the bail over to fit
around the heart. Cut a piece of tubing so that you have a bit to
work with at each end (sticking out past the holes in the bail on
either side). Flare one end of the tubing by rotating a scriber in
the opening, and then assemble the bail. Flare the other end of the
tubing, and gently peen the ends over, turning the bail over once or
twice to see that both sides come out even.
There is a much better description of this process, with lovely
photographs, in Elizabeth Oliver’s "Jewelry Making Techniques Book."
You could probably do the same thing with a plain wire rivet, but the
tube rivet is, I think, a little easier on the stone, and will look
5949 Calmhaven Drive
Cincinnati, Ohio 45248