The thing to understand about conventional battery chargers is they really aren't voltage regulated. They rely on the battery itself to limit the voltage. So if you hook any conventional charger to a battery long enough you'll overcharge the battery. And of course the smaller the battery the shorter the time before it's overcharged.
Your "2 amp" battery is actually a 2 ampere-HOUR battery. Meaning that fully charged it can theoretically source one amp for about two hours. (Actually not, but let's not go down that rabbit hole.) So, it's probably safe to charge it with your six volt 2 amp charger as long as you don't leave it on the charger for too long. A couple of hours is probably fine, but leave it charging overnight it's likely to get overcharged. The safest way is to monitor the battery voltage with a meter and take it off the charger once the battery gets up around 7 volts (while under charge).
There's no simple way to drop the voltage of your 12 volt trickle charger. If you install a resistor in series with the battery, it will drop the voltage but as the battery's charge increases the voltage drop across the resistor will fall, which is exactly what you don't want. You could put a 7 volt zener diode in series with the battery, but you'd need a zener capable of dissipating about 7 watts. (The 1N5342 zener diode is a 6.8 volt, 5 watt zener; give it a shot and let us know how it worked.)
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Today's Featured Article - Choosin, Mounting and Using a Bush Hog Type Mower - by Francis Robinson. Looking around at my new neighbors, most of whom are city raised and have recently acquired their first mini-farms of five to fifteen acres and also from reading questions ask at various discussion sites on the web it is frighteningly apparent that a great many guys (and a few gals) are learning by trial and error and mostly error how to use a very dangerous piece of farm equipment. It is also very apparent that these folks are getting a lot of very poor and often very dangerous advice fro
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