Michael, if you are talking about a normal point and shoot camera then yes it can be done. But requires a bit more patience and setting up.. First of all a round bowl always works the worst. The measuring tub works best as the koi always goes back and forth giving is less of a chance to do laps round and a round. If you got a rectangular tub then great! then if not then round will do.
Fill the tub up with water at least 2 inches paste the tail fin. What we are trying to do it have the koi no swim up and down but also not disturbing the top of the water so it doesn't give a wrinkle effect. In doing so its best to have a friend around to keep an eye on the jumper...
Back to the camera.. If there is anyway you can attatch a polarizing filter to your camera then by all means do so. If you cannot then hold one in front of it. This will eliminate the glare off the water.. Which leads us into the next phase. The tub must be put under a "consistent" amount of shade so the sun is not bouncing of of it. I suggest under a patio as long as it is shaded. also to take the picture during dusk and or dawn times of the day. The suns light is not as strong and your flash unit will take care of the lighting situation..
So say your set up now and ready point and shoot. put the koi in the tub. Pop all the bubbles and such on top of surface of water. Try to clean any of the debris in the water as well. If you got a friend or spouse then have them near the tub. When the koi gets stuck on the sides then have em direct the koi away from tub.
Be patient and try not to move so much let the koi calm down and also anticipate the koi as it swims towards you. I always like to this of the koi gliding with its wings spread out and tail perfectly straight. Take the shot at around approximate 45 degree angle. some koi do better a little above depending on the pattern.
If ya got the Pounds then spread for a Digital SLR camera. Once you do you will eliminate many headaches.
Many more tricks to taking photos and I just touched on a few that popped up in my head..
Joe