I have a Coherent FAP800 with a 40 watt bar in it and I have been experimenting with a 60 amp CC power supply by driving it to full output at about 2 VDC without the current limiting turned down to keep the current below 50 amps and it ran just fine
without heating up so much the current would begin to creep up, but I do have a very good heat sink on it too.
I then drove the bar directly with a Cyclon 2 VDC round lead acid battery cell which can supply hundreds of amps and had no problems with it. I suppose if the unit isn't heat sinked well enough the current would start to increase above the maximum recommended, but I never had a problem hooking it directly up to a battery without a CC driver using my 5 pound heat sink with fins on it. Would I recommend this? No, I'm just telling you what I experienced.
Edit: I'm back to add more info....
There is a LPF member using a Texas Instruments buck on a 40 watt Coherent bar and although it isn't a constant current regulator, it's working well for him. He's trying to wire it up using the sense leads and a resistor to keep it from changing current, not sure what twists he is using to do that. However, you might look at this as a possible driver, you can input up to 14 VDC and it will produce up to 50 amps out from .7 to 3.6 VDC, but you will have to use two of them for your bars, the output voltage isn't high enough to run them in series. I don't think they are very expensive and they run cool due to their high efficiency.
Constant voltage (not constant current) buck:
http://www.ti.com/product/pth08t250w
I have a power supply much like Cyparagon offered you and it works well for me, you can run two bars in series with it and set the current too. His price is good.