Basic 24hour on/off timer

Why don't you put the batteries in parallel and trickle charge both at the
same time?

What happens when I put a used battery on the charger with a full one?  Will
it just trickle and not fully charge the empty one?

Just isolate the two batteries by joining the negatives together and
feed the charger through two diodes, one to each positive.

if it is an intelligent charger, and needs to measure terminal voltage
etc, this will create a major problem

The way for many people here would be to set up a simple PIC circuit,
driving a relay to do the job, or use a 555 timer that outputs a pulse
every 5 seconds into a  4020 binary counter.   You could then use the
/16.384 pin 3 to power the relay via a suitable transistor. This would
give a changeover approximately every 24 hours.  (The 4060 even has
its own inbuilt oscillator, so it would be even simpler to get up and
running :)
http://www.kpsec.freeuk.com/components/cmos.htm#4020



However If you want it ultra simple, cheap, and fast and 12 hours a
battery is ok, go to Bunnings, buy one of those $5 mechanical timers
intended for mains appliances, set it to 12 hours on/12 hours off, and
use it to power a relay to switch between the 2 batteries, I think
this would be the cheapest and most reliable (set and forget) system
for you.   Also if there is a blackout, the timer will remember its
position, and the battery will still end up with the same number of
hours of charge.

as for a relay, I would use one of those 12v high-current automotive
relays, power it from a 12vdc plugpack that you plug into the timer
directly.

If your like the rest of us, you would probably have a +12v dc
plugpack lying around, or would be able to buy one for a few bucks
from your local electrical store/pawnbroker etc.  

If you want an indication of whether the relay is on or off, you could
add a LED with a 1k resistor in series, or a small 12v bulb across the
relay coil terminals.

---------------IMPORTANT (for car batteries) -------------------
Finally, keep the relay (and timer) away from the battery if possible,
or put them in a sealed enclosure, since some batteries emit a
flammable gas when charging, and a spark from relay/timer contacts
opening and closing might be enough to ignite the gas and start a
fire.