That looks like a bridge or half bridge rectifier (bridge I would guess).
I agree with Olin's comment about maybe needing a series resistor.
The magnetics look like they could be designed to have a very high leakage inductance so it may be kind of a constant current charger. I have a hunch there is something interesting going on there, it may also be saturable to limit the terminal voltage of the charge.
Typically Se rectifiers have a forward drop of about 1V per junction, so if there is only one junction or two per diode, then 2 or 3 (respectively) Si diodes in series for each Se diode would be reasonably close.
The nameplate indicates up to a couple amperes, so maybe some 1N5404 3A diodes would work for you. Quite possibly the 2.4 on the Se rectifier stack refers to the current rating, and perhaps 16V is the voltage rating.
Needless to say, if you fiddle with the diodes and don't get it right, you could create charging parameters that damage (or fail to properly charge) a battery. Murphy's law (and Vf voltages) would make the former more likely.
If it has that characteristic horrible (and apparently toxic) rotten garlic/onions smell that Se rectifiers give off when they are dying you can be pretty sure it needs to be replaced.