Subject: How large/what capacitor(s) do i need do supply 2A 19.2V for 0.1 sec

I am trying to drive a solenoid (13.8V dc 20W). I have a 'timer' (not sure how 
it works, but it does) which requires a constant 13.8V to give me the time i 
require. I have built a variable regulator to give me this voltage (about 
19V in-certainly more than 16V-up to 24).
    I am told that a most normal batteries wont be able to supply a load of 2A. 
Is this true? My conclusion to get around this is to 'buffer' some energy in a 
capacitor, so the battery only has to charge the capacitor, and the capacitor 
can supply the peak energy flow.
    I only have to draw this energy 20-30 times in a day (not every day either), 
certainly no more than 60 times, so 2A by 6 seconds gives 200mAH? and i am 
thinking of using 1000+mAH remote control car battery packs- 2 lots of prepacked 
8x1.2V cells. (or any other ideas) and charge them using a charger of course 
(electronics is not my forte-Molecular Biology is)
   So can capacitors do this? and i can get away with  cheaper NiMH or NiCad 
batteries (even it it is up to about 1kg of batteries) or do i *need* to 
purchase a very heavy (id guess >3kg) (and expensive) sealed lead acid battery 
and draw the current directly. Or am i just wasting my time and i should be 
tethered to the mains power while im standing in puddles in the glasshouse?

Re: How large/what capacitor(s) do i need do supply 2A 19.2V for 0.1 sec