Power supplies would really be better named power converters. It sounds like what you have is a power supply that converts AC to 19V, but you need 12V, and you are thinking that converting from 19V to 12V will be easier, cheaper, or somehow better than converting from AC directly to 12V.
There are devices that will do this. The simplest is a linear regulator, which will convert the excess energy from the excess voltage into heat. This is not practical at your design current: a linear regulator would create \$ (19V-12V) 10A = 70W \$. This is quite a lot of energy to waste, and simply keeping it cool will be hard.
There are DC-DC buck converters that can do this more efficiently, and this would be the solution if you had to power your device from 19V.
However, it sounds like the 19V supply isn't a hard requirement in your case, but rather you are assuming using it will be better. This isn't really the case. It doesn't matter if you are converting from 19VDC or 120VAC, the problem is the same: you need a power supply. However, converting from 120VAC directly to 12VDC will be more efficient, and since 12VDC supplies are so ubiquitous, it will probably be easier and cheaper to find this supply than a DC-DC buck converter that meets your specifications.
I would further advise that you purchase, rather than build the 12VDC supply. You probably won't save much money doing it yourself, and it's much safer to get one that's been designed by an experienced engineer and been put through a safety certification process.