This can be done with a small water pump on a timer with 15-20 minutes per day, but.... a 5 gallon bucket for 4 plants won't last more than a day, two tops. Carrying 5 gallons up and down attic stairs can also be a real pain in the ass.

If your going the water pump route anyway, I would find a way to have a 30-50 gallon bucket on the main floor near a water source, and then just run your tubing through the ceiling to your plants. Its definitely doable, but not just with gravity, you'd surely need a pump and timer. You can get a cheap water pump for $10 and a timer for $2-5. Just the fact that you can keep from toting water up and down the attic would pay for itself in a day.

Good luck!