If your jeans are made of mostly cotton, then the best choice would be a fiber reactive dye. Fiber reactive dyes are easier to use than all-purpose dyes such as Rit, and they will keep their color for years longer without fading. Don't use Rit dye, because it fades quickly and bleeds every time you wash it. For long-lasting, good-looking results, in North America, use Procion MX dye in a top-loader washing machine, along with salt and soda ash. (See the link to the instructions page below.) In Europe or Australia, use Dylon Machine Dye, which is a similar kind of dye formulated for use in front-loading washing machines; you cannot buy Dylon Machine Dye in North America, though.
Dye is transparent, so you need to select a color that will incorporate the existing pink color. Black will work well, but you'll have to use two to four times as much dye to get a good dark black, regardless of what type of dye you use. Purple, red, navy blue, or orange will work well, too. You will not be able to dye pink to make it yellow or bright green.
Unfortunately, the stitching that holds the seams together is almost certainly made of polyester, which means that it will not take the dye at all. The thread will remain the original color, while the fabric changes to whatever color you dye it. Choose your dye color so that the stitching will not stand out too badly.