No not a task for a professional Lapidary, but it might be more
expensive than you want if you don’t use the items often. Yes, pretty
much any diamond or Carbide coated bit would work. Just remember
drilling stone is pretty slow and you can’t use a lot of pressure.
When drilling rock, I have found it better to lift the bit from the
bottom of the work often to let water in and sludge out.
A hand electric drill or drill press may be used, I would use a
hollow core bit for a 1/2 or 1 inch hole, but as you did not say how
thick these items were, I am only guessing they are thick enough to
drill into and break the core out with damage to the hearts. Yes, you
will need a supply of water when you are drilling, otherwise you will
destroy the bit and have to buy more.
Alternate suggestion - Drill smaller holes around the edge, and use
a threaded screw, like a 6 or 8 and drill in 1/2 inch and epoxy, you
could get by with a much smaller bit, but you will have to drill more
holes, but then you could just bolt it on to the box.
Last suggestion - If the stones are that large make a
copper/nickel/brass bezel and drill in from the sides in a couple of
locations and you could use pins to hold it in making a stronger
mechanical bond and less reliance on glue. The copper plate could be
attached to the box by any number of means and the hearts set in.
Sounds like an interesting project, good luck to you and your