Dd is 25mos, and we have had the same problem with constipation. We actually switched peds over this as I felt our old ped wasn't taking the problem seriously (not to mention different docs in the practice were giving contradictory advice). The best advice we got was actually from a friend's ped and that was to give her a dose of milk of magnesia once a day, which we did for about 6mos. She was 18mos at the time, and the dose was 1tsp per day. For the first month or so she would just drink it straight (try the flavored kind), and once she started refusing it, we would mix the unflavored kind into her morning oatmeal (also mixed it in pudding, yogurt, and mac+cheese). When she was in a bad spell, we would use a suppository if she hadn't had a bm in 48hrs.
She is off the MOM now (I forgot to pack it at Christmas and she did ok), but I do make sure she gets fiber for breakfast. Luckily oatmeal and bran flakes are her two favorite breakfast foods. Be advised though that raisin bran has lots of added sugar, so I just add my own raisins to bran flakes. However, all the fiber in the world won't help without enough water. At her 2yr checkup, our ped rec'd 24oz of milk AND 12oz of water per day. When she is not drinking enough, I feed her lots of high-water fruits like grapes and melon. Soups are another way to sneak in liquid.
I need to go make lunch for dd, but I'll try and post back later.