Making a diaphragm spring out of sheet metal
This is a little speculative as I haven't tried it with phosphor bronze, or anything as thin as you got.

First cut a circular piece, and clamp it between 2 rings.  A holesaw and scrap plywood (to support it and to make the rings) may be helpful here, but you don't yet want a big hole in the middle of the workpiece.  Mark the centre accurately, a set of equally-spaced radial lines (I suggest 12), and a  circle a little smaller than the inner diameter of your clamp rings.

Then beat or even press it into a conical shape, using a round-ended tool in the middle (maybe even the blunt end of an old drill bit).  You should have a cone with a slight brim round the edge.  

Now drill out the centre hole (using a step drill or cone drill would be best).  This is already a spring, but perhaps rather too stiff - this is a good time to test.  Cut along 3 of the 12 lines (equally spaced) and test again.  If it's too stiff, cut along another 3 lines so every other line is cut, test again, and if necessary cut the last 6 lines.  For the cutting, I'd use a hacksaw with something supporting the workpiece, as you want to remove a little material.  You might be able to use tin snips and make two parallel cuts (my tin snips are heavy duty and not fine enough for this).

If you want it to be flat around the centre hole, instead of using a round-ended tool, drill a small hole and use that to clamp discs front an back, then apply pressure to the discs.

The important bit is to keep everything concentric - you'll probably spent more time jigging than actually making the part.