Ok, this is totally gross but... My son, when he was 3, would pee in the potty and ask for a diaper when he needed to poop. I accommodated, because everyone says let them get there when they're ready. Until we went to an amusement park and I forgot to bring diapers in with us. Between every line and ride he was crying to go to the bathroom but then we would get there and he wouldn't do anything. He would just sit on the potty and whine that he needed a diaper. I begged, pleaded, cajoled, nothing worked. He would get up and have done nothing. We would go back out, meet up with everyone, stand in line and he would start crying again, that he HAD to go! So back to the bathrooms, repeat chorus. Finally, he couldn't hold it in anymore and he messed his pants, but just a little bit. So back to the bathrooms, clean him up, beg him to go in the potty, rinsed out his undies, dried them under the hand dryer, back out again. We did this for HOURS. I swear, that child pooped across the entire park. Finally, FINALLY, he had released enough to be done, near the end he got some of it in the toilet because my dad made him sit there while he cleaned his underwear again (me & hubby were on a ride at the time). But, this seemed to break the diaper cycle and he never had a problem again. So, it was ugly, and very hard, but not having the option of the diaper was what finally put him pooping on the potty. ---suggestion? carry a change of undies & pants and then take him out for the day without diapers. Then he doesn't have an option except to go in the potty and you have a spare set of clothes if he messes his pants.
My daughter on the other hand, was fairly easy. When she decided to start going, she just went. She peed on the potty for a week, and then I took her to the store for a "good job" present for peeing in the potty. I let her pick out a second gift too. When we got home, she only got to open one gift. The other went up on the shelf and I told her when she made poop in the potty, she could have that one. Within a couple days, she yelled for me to come to the bathroom and sure enough! Success! There was much celebrating and hoopla, and she got her special toy and we've not had even one accident since. ---suggestion? reward for positive behavior.