One Apple Cinema 30inch display has a native resolution of 2560x1600 if you are trying to run two of these monitors in eyefinity mode you wont be able to get full resolution (5120x1600) on both since the HD 6870's max resolution is 2560x1600
Also I'm not sure what you mean by "standard Apple Cinema Display cables" if you mean your using two-dual-link DVI cables those are the right cables for a resolution of 2560x1600.
The problem is the 6870 only has one dual-link DVI port the other DVI port is a single-link DVI port.
Dual-link DVI is capable of 2560x1600 but, single-link DVI is only capable of 1920x1200 so even if your just trying to run the 2nd monitor in cloned or extended mode you wont be able to reach a resolution of 2560x1600.
Your HD 6870 should have a displayport or mini-displayport(s) these are capable of your monitors full 2560x1600 resolution. You could try using your video cards dual-link DVI port and one of these or if your 6870 has two mini-displayports like mine you could just use them both.
If your monitors don't have any displayport connections you will need to get a mini-displayport to dual-link DVI adapter or displayport to dual-link DVI adapter if your using a displayport and not the "mini" or two if your using both mini-displayports.
The Apple store sells them here:
http://store.apple.com/us/product/MB571Z/A You can find cheaper and possibly better ones if you stay away from the Apple store, just make sure it's to "Dual-Link" DVI