Battery testing and devices
You are correct in that simply measuring the open circuit voltage across a battery is not an accurate indication of whether it is good or bad. 

As most batteries begin to fail their equivalent series resistance (ESR) increases. As the ESR increases, it creates more of a voltage drop on the output of the battery proportional to the current being drawn. For example an ESR of 500 mOhms will drop only 50 millivolts with a 100mA load, whereas an ESR of 1 ohm will drop 100 millivolts with a 100mA load. As the battery continues to fail the ESR often continues to increase, and the chemical composition begins to break down making it more difficult for the battery to supply the power necessary to drive the 100mA load. 

Measuring the open circuit voltage across a battery draws practically no current (the meter is a very high impedance) so the drop across the ESR is barely seen. You would not be able to tell the difference between a 200 mOhm ESR and a 1000 mOhm ESR simply by measuring the voltage without drawing current. By connecting a fixed load across the battery you will get a better idea of how high the ESR is, and whether or not the battery is good or bad.

To answer your questions, yes: Meters do exist that apply a load before measuring the voltage. Also, yes: You can build your own. We cannot tell you where to buy existing meters because that is considered off-topic for this site. I can tell you, however, that they are out there and you just need to do your research to make sure that the tester you end up buying does apply a load to the battery under test.