Car batteries, being lead acid, are 'constant voltage' charge, meaning, unlike nicads or Nimh, that no constant current limiter is needed, and as full charge is reached, the battery voltage rises, opposing the charger, and reducing the current flowing to a safe value. Therefore once started they can be left floating on a constant voltage charger almost indefinitly without damage. Parallel charging for
lead acid cells only will be OK if the two batteries have a similar state of charge before being connected together (and the same voltage of course...)
If one goes down however, it will likely bring the good one down with it, as the full one will flatten through the bad one, so putting old and new in tandem is a bad idea !
In short, charge them both up fully, then put them in paralell, and treat as one battery for charge and discharge. Periodically seperate the connections and check that they are behaving similarly .
I'd add a large (100A?) fuse as a fire stopper in series with each individually, although only 12V in to a low impedance a good car battery can supply 1000A long enough to set fire to your clothing and start the acid boiling inside, possibly splitting the casing too- this can be a touch inconvenient, particularly indoors.
(I have only done it once
)
regards M.
An aside If you'd said NiCd or NiMh then the answer would have been NO series charge only.