The best paint I can recommend for your job is Colortrend Satinwood or Eggshell finish. It's water based and goes on beautifully. It's also tough as old boots and will stand up to the wear and tear in a kitchen.
Disclaimer! I'm not connected in any way to Colortrend, but I haven't used any other paint in my house for 20 years. I think its fantastic stuff.
Whether or not you decide to use the Colortrend, the one thing you might find when painting over treated wood is that it takes quite a while for the paint to 'cure'. The paint may remain 'tacky' for up to a week so give it plenty of time before you put the doors back on.
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