It is a pretty small pump, I believe it draws 10 amps. It is an on demand pump that will draw water out of a tank and send to the toilet cycling everytime the toilet is flushed.I am trying to avoid having to have a battery and charger to run it.
Then there are possibly thousands of single output DC power supplies that could meet your needs. Your application isn't one that requires 10A continuously, but probably needs more than 10A for short periods. Things to consider along with environmental and any required listings. Also consider the use of an appropriately sized flyback diode at the pump.
If this is something you are selling to a customer? I would get the supply the manufacturer specifies for the product. If you are just experimenting/inventing at home, Ebay has several supplies for around $40-50 shipped if you look at "12vdc 10 amp power supply".
Eliminate the battery and just use a 10 amp charger.
Nope, very bad idea. Most chargers will either put out too much voltage (they often have a high voltage start on charging and taper down as the battery charges), have excessive ripple current which can affect the motor's life, and often have very poor current/voltage regulation abilities.
Finally, a 10 amp or greater charger will often cost more than the 10 amp power supplies available from eBay, Mouser, DigiKey, etc.
If you're dead set on using a charger you'll need to do something to dampen the ripple and stabilize the voltage. Without opening the charger and doing a bunch of calculations to figure out exactly what to put inside; the easy way is to run the motor off of a battery that is being constantly charged by an off-the-shelf battery charger.
But I agree that you will likely spend more time and effort than just biting the bullet and buying a proper power supply.
BTW, don't forget about the inrush current required start the motor when you're figuring out how many amps you are going to need.