Try each card on their own and see how things go. I know these cards can draw a massive amount of power for a short time before failure. Up to 550w before the fuses go out. Use only the latest drivers and keep the fans at a high setting.
I've tested each of the cards using heaven and 3dmark11 which did not cause it to beep. Also tested using 2 hd 6990 in xfire using both programs and did not get the beeps. Its only when I use sli with the gtx 590 that I get the beeps. I would think that the hd 6990 draw just as much power as the gtx 590.