Charge a 24volt battery with two 12 volt chargers???

I don't know of anyway to do it automatically.

If you are manually charging the batteries, you can kill all the loads, break the series connection between the batteries, charge what are now two 12 volt batteries, and the re-establish the series connection after charging is complete.

This should be an "emergency" type practice rather than a regular thing. Your battery life is better if you charge the whole bank as one unit rather than as two seperate units.

"Can anyone give me a valid technical reason why it won't work."

What do you mean by it ? 

If you mean connecting the chargers in series, you run a risk of the control circuits not working properly. The batteries may not charge at all. You could also end up with uneven charging of the batteries, or frying the batteries. There is also a good risk of pushing to much amperage through the control circuits, which could fry your chargers. There are a lot of different logic circuits used in battery chargers, different ones will react differently.

If you meant splitting the batteries, the risk is that if the two chargers charge at slightly different rates, you end up with the batteries eqaulizing the charge between them, the first time you put a load on them. This gives you a high discharge rate (and an energy loss). Repeated cycles of this higher than normal discharge rate shortens battery life.

If you are careful to charge the batteries as evenly as possible, this shortening of life may be minor. But as an example, suppose you only get 54 months instead of 60 months of life out of them. Is it worth the risk ? 
As long as your willing to accept the risk, and live with the no loads during charging, there is no technical reason to prevent it.

I think if it were my system, I would spring for the 24V charger. But, if I was trying to get by with the two 12 volts, I would probably install a knife switch in the series connection.