If you wire them in series to get a 12-volt battery, you need a 12-volt battery charger, unless you want to unhook the two 6-volt batteries and make them separate batteries each time you want to charge them. '
Pro Charging Systems can be confusing with their terminology, but that's because their chargers are for boats, mostly, and with most boats all those battery banks are indeed separate banks, and are usually made up of individual batteries. When you use those chargers in a situation like ours (or on a boat with larger battery banks), then things need to be looked at a little differently with respect to terminology.
A 6-volt battery has three cells, and a 12-volt battery has six cells. When you put two 6-volt batteries together you have a six cell battery at 12-volts. The key thing to keep in mind is, when you connect two 6-volt batteries together to create a single 12-volt battery, you no longer have two 6-volt batteries. You have one 12-volt battery. Treat it as such.
The Pro Charging Systems terminology kind of messed me up when I got a single bank charger (because I only have the one house bank). The On-The-Run chargers, just like yours, come in one, two and three bank versions. Each output lead (cable) of the charger is 10 amps. So, with a two bank charger, you connect one lead to one battery (or battery bank) and the other to another battery, and each lead will feed each battery bank 10 amps independently.
Again, with two 6-volt batteries wired in series, you don't have two separate batteries, you have just the one 12-volt battery. Soooo...
Here's the kicker. Instead of connecting one lead to one battery and the other lead to the other battery, you simply connect both leads to one battery bank and you'll get 20 amps flowing to the bank.
Where I got messed up with the DualPro is, because I only have a single battery bank, I got a single bank charger. It outputs 10 amps. Unlike a direct connection to the alternator which can throw scores of amps to the battery bank, when the alternator is powering the DualPro charger, the charger only sends 10 amps to the battery bank. That's a problem when the fridge and other stuff is pulling 12-15 amps while driving down the road.
So I need a 3-bank On-The-Run charger that has three independent outputs, which are all are connected to the one bank, and the charger will output 30 amps to the bank.
In your case, simply connect both outputs from the charger to a single terminal on the battery bank, and it'll output 20 amps to the battery bank. Connect both negative leads to the same ground, as well.