Aside from blurring it, you could also try to make the border thicker. If it’s just a graphic from Photoshop, it could be fairly easy to do..
But Darby is right and it’s something for you to think about in the future. Anything close to 1 pixel will always jump around like that. It will even happen if your fonts are too small, especially with serif fonts. So basically, the thicker the better when it comes to TV display. If it’s only intended to be viewed on the computer, it’s not such an issue.