Hi B.,
Not everything works for every child, but I will tell you what we did. When our 2-year-old asked for a diaper to poop in, we obliged for a couple months. He was already pee trained, including at night. At one point I decided it was time to force the issue (we had a newborn at home). We just started saying no when he wanted a diaper. He is just as stubborn as we are, so he would go a few days holding his poop when we knew he had to go. He would hold it so long that he'd barely make it to the toilet (and had about 2 or 3 floor accidents), but he would use the toilet because his bowel movement was very imminent. THen he would see how "easy" it was. We rewarded him with a sweet treat every time he went on the toilet or even put in a good faith effort. As time went on, he spent less time thinking about and arguing about using the toilet to go #2 especially since we were totally consistent once my husband and I decided it was time. Most people give in and I don't fault them for it.
One day he had a stomach bug. That was a turning point because he had no time to argue or hold his poop. So getting ill was a blessing in disguise. Obviously you can't predict a stomach virus, however I hav heard that others have had success toilet training at times like that. Unfortunately, most toddlers get nasty stomach viruses once or twice, esp. those in daycare, so if you're lucky (or unlucky however you want to see it)...
Oh, and I should say that our ped had us give him a little Miralax (other things work as well such as prunes, etc) to soften his stool since having big hard stools deters little ones from wanting to go. Make sure you check with a professional of course.