Hi Paul,
Breeding corys is not difficult, in fact many people do it by mistake.
The females are invariably larger than the male, longer and wider in the body, quite noticably usually. They don't really have many specific requirements, but a pH somewhere around neutral will be fine, sand as a substrate is really essential, and they will appreciate places to hide. Live plants always make them feel at home.
Also, try to have a shoal of at least 6 corys. They are shoaling fish and feel much more comfortable in numbers.
Some corys prefer cooler temperatures, for example peppered corys (Corydoras Paleatus), so check which ones you have.
They breath atmospheric air by regularly swimming to the surface, so a shallow(ish) tank is preferable (certainly not over 2ft deep, preferably under 18 inches).
Spawning is easily induced by lowering the temperature of the tank by a few degrees. This is usually done with a large water change (70 - 80%). When the water starts to heat back up, let the spawning commence.
I'm not sure about the blue stomach. Maybe someone else will have a better idea on that?
Hope this helps.
BTT