If you want to be able to run both chargers at full capacity, you'll need a power supply that puts out about 20% more watts than both chargers combined power output. This 20% takes care of the inefficiences in the chargers.

Your charger has 120watts output power. So if you bought another charger with 120watt, you'd need a PS with 288watts (1.2 x 240watts). If the PS supplies 13.8v (like a lot do - both of mine are 13.8v), then it would need to supply 20.9 amps. A 20amp supply would be plenty close enough and work just fine.