EBAY has cheap diamond core drilling bits.

A core drilling drill is like a drill press with with a rubber suction base and a water pump.

That wouldn't do what you need any way. A slow drill --plugged into a gcfi outlett ---and a hose set to a dribble is the way.

By the way--good quality core bits cost$$$ We figure about $100. per inch. 2" bit $200--6"--$600

Makes for an expensive hole--I've never tried the cheap Chinese bits--Might be fine for a few holes.
-----Mike------

 

From experience, having done this: They do make core drills which use suction type bases, these won't work for your project. They do make core drill with use "Hilti" type anchors to hold the base in place while drilling, this works better on rough surfaces. These are available for rent at most equipment rental places. You may have to prove/convince them that you have experience with these. You will also have to sign for the wear/tear on the bits, or even agree to pay for one if it breaks. EXPENSIVE! Drilling 10" deep into poured concrete (rebar?) can be done, but slowly. You will be using water as the machine requires it. IF the concrete is more than the 10" deep and you only want to go 10" deep, then drill to that depth, pull out, and smack the plug with a sledge hammer directly on top of the plug. This has worked for me to break the bottom of the plug loose. Use a "Hilti" type anchor drilled into the plug for removal. We set many safety guard rails into place in an 18" deep concrete floor this way. The 2" holes should be easy enough. David