This is the replacement battery. It's a VARTA MC621. It's a Lithium Ion rechargeable battery
it's 3.0 volts
it's 3.0 mAH (milliamps)
It measures 6.8 mm in diameter
It measures 2.15 mm in height.
This online battery retailer (Apex Batteries) had it, but it was obfuscated with a really long part number including some superfluous information.
http://www.apexbattery.com/mc62160621-101-511--rechargable-lithium-battery-lithium-batteries.html or http://tinyurl.com/58j3s7
They have it listed as
MC62160621-101-511 - Rechargable Lithium Battery
I'm told that any 3 volt battery LI battery would work, and possibly give longer life, but I'm too anal and clueless about this stuff to do that.