Geoff, if your piece is really made of solid teak, and you want it to look like pine, it never will. You might get the color close, which will be difficult, dangerous, messy and expensive, but it would never look like pine. The grain and character of the woods are too different.
With a lot of practice, you could learn to faux paint one kind of wood to look like another. I have seen metal doors that were painted to look like wood and you had to get real close or bang on them to tell the difference. But when you did, it was immediately apparent. And one paint chip spoiled the effect. And why would you go to all the trouble on what could be a beautiful teak piece? Teak is also a much more expensive wood than pine. Real antique pine wood and furniture is expensive but you can't paint on or stain on antique value.