Just in case you didnt get this from the first posting:
I'm a speech pathologist who pecializes in feeding difficulties. Still being on a bottle at 15 months qualifies as a difficulty.
We have a recommended program we follow. If you send me a fax number, I can fax you the information.
About his teeth: Sippy cups/bottles ruining teeth is a myth. Just think of how many years people have to wear braces to get their teeth to move. And what force and pain goes into moving them. The cumulative amount of time a child drinks per day amounts to minutes. And they aren't exerting pressure on their teeth while they do in; not in any amount that will move their teeth.
The problem with bottles and sippy cups being used too long is primarily the social stigma, and secondly, there is the lack or correct motor development in the mouth. The way babies transition to baby, to table food over time build up the muscles needed for correct speech production and moving on to eating a wider variety of food.
My major concern for kids who haven't weaned is that they very frequently become the significantly picky eaters we see in the clinic...kids who will eat only one thing..or only a hand full of things. If your child is still drinking breast milk, you must make sure he isn't drinking so much that he is limiting other foods. Brest milk can be a supplemental drink at this point, but doesn't have the required nutritional content for a child of his age.
So..having never seen him an dnot knowing any of the nutritional aspects going on...after we assess the muscles of the mouth adn determine the problem isnt in his mouth, there are a few cups we try first...
Rubermaid makes what they call a "juice box" You find it with Rubermaid items and not with sippy cups. It is a short, rectangular bottle with a hard plastic "straw" that flips up and down. This is a great cup to work with first. When you first introduce it, you can sqweeze it a bit to make the juice come out the top so he can taste and understand how it works.
A second option that works well is simply taking the valve out of the sippy cup you already have. This will defeat the purpose of the no-spill option because without the valve, if the cup is dropped, it will spill. But it teaches kids HOW to drink out of this type of cup. And after a while, you just pop the valve back into the cup.
Also, you CAN and should start him on a "real" cup. I'd only do this with small amounts of water while you're outside playing! It will be messy!
Drinking from the breast at birth is instinctive. After a while, kids learn how to suck/swallow/breath and the reflex goes away and it becomes a learned behavior. All other eating/feeding experiences are learned. Kids have to be taught to eat. And transitioning to a sippy cup (although NOT essential development wise...I'm a mom, so I know its essential SANITY wise for moms who are tired of cleaning juice off the floor!)is a learned behavior. So you just need to teach him how to do it.
We find we typically only see the kids/moms in our clinic who are at their wits end with feeding issues. But assisting with all these baby steps along the way is what a feeding therapist can do as well...keeping you out of crisis mode in the future!
Oh, and a small amount of coughing is to be expected. The first few times your child tries a big cup, or a sippy cup with no valve. He should learn that taking too much makes him choke so he'll adjust the amount he takes for next time until he's a pro. If he doesn't "learn" to adjust the amount he takes in and continues to choke, then you may want to consider a feeding assessment to make sure all muscles in his mouth are developing correctly. You'll need to make sure the speech therapist you see specializes in feeding therapy.
Good luck!
I'm editing my initial response by adding this after reading the other replies. Almost always, it can work by just removing the bottle all together. It causes stress, though. And if there is a motoric issues at all...it wont work. If he cant physically handle the cup or doesn't have the learned skills necessary to use the cup, he wont be able to take the sippy cup, even if he wants to! So then you've created an even bigger problem. Like i said, this almost always works and moms who do it certainly aren't wrong. But if you do take steps to train him on the next level of eating, which is transitioning from sucking to drinking and controlling larger amounts of liquid, you have taught the skill and eliminated the need for it to be stressful for either of you.