I had a monster case of constipation from Gleevec that went on for 18 months. It can be a real nuisance. Now that I'm on Sprycel, the issues have subsided, thankfully.
Nevertheless, I will share advice based on my experiences. I figured out how to beat severe chronic constipation, but if I lapsed on my routines, it would come back in a day. Here goes:
Move around a little more, perhaps taking walks or light jogging. You wanna keep your guts in motion.
Drink more water.
Eat less dairy.
Add healthy whole grains to your diet, such as high-fiber breads and brown rice (a rice cooker is your best friend if you have chronic constipation).
Add some dark greek veggies to your diet. Spinach, kale, broccoli. These will also replace the calcium and vitamins that you're not getting from a reduced dairy diet, and they're loaded with fiber.
Add some psyllium husks to your diet, such as sugar free Metamucil or psyllium in the pill form.
Or you can try ducosate sodium stool softeners, such as Colase. They will make your GI tract retain water, and that will keep stool moist and soft.
Remember that certain fruits, such as apples and pears, contain a healthy, natural laxative called sorbitol. These fruit also contain insoluble fiber, which will help too.
Be very, very careful with stimulant laxatives. You can build a dependance to them, where your gut stops pushing the food along (peristalsis) without the laxative. Stimulant laxatives are actually quite dangerous if used frequently. They are NOT a long-term solution.