Charging 2 li-ion batteries in series
You cannot use 9V/12V and plug chargers in series. You need to use 5V and connect them in parallel.
Imagine that you connect them serially to 10V, and one of batteries is fully charged and the second one fully discharged. Then the first charger won't take any current and the second one will need 1A, it is not going to work, because the first charger will block current and almost whole 10V will be on this charger.  

So you have to use that 5V regulator.  

UPDATE:
Your second link is for 2 cells, so yes, that is better solution than 2 separate chargers.