I knit Continental as my preferred knitting style. But I also know how to knit English style. There is a way to catch the unused color in every few stitches to bring it along to where it will be needed. But...it uses both methods of knitting, kind of. You don't really knit the English way necessarily but you do use both hands. It's a little complicated to describe. Here is a link to a site that shows how to do it. LINK
There is more about handling 2 colors on this page, but you want to look down to the 3rd page (its a PDF file) to a part called Wrapping the Yarn While You Knit.
There may be other ways, some that are even simpler but this is real slick once you learn it.