Unless you are recording in a very controlled environment, I would recommend a contact mic (which is, ultimately, a better-sounding stethoscope). A standard capsule-based mic will likely generate too much noise (or pick up noise from the surrounding area) because you'll need to turn it up significantly to pick up a pulse.
Check these out: http://www.c-ducer.com/
They are contact mics that could easily be mistaken for medical electrodes but anyone who doesn't know better (it basically feels like a leather strip, and it comes with its own double-sided tape). I own a pair and they sound fantastic — very low noise and they come in a kit with a phantom-powered impedance convertor that terminates in a standard XLR to plug in to any preamp. They're advertised for violin, harp, piano, and any instrument where there is a resonant body. Properly fitted to the upper chest and/or neck, I'm sure you could get some good heartbeat sounds.