Javascript generate transparent 1X1 pixel in dataURL format

I would like to know a way to generate a single pixel in JavaScript converting it to base64. The ideal function would be:

function createPixel(hexColor, opacity){
   //...Calculate
   return base64DataURL;
}

I am not very familiar with image processing. Any format is fine (png, gif etc). I would like to use this to overlay background images, (yes I could use rgba css3 but I am trying to place it with a background-image only on one element so i am not overlaying an element on top of another to achieve the effect).

Thanks in advance.

Edit: I would like not to use canvas, I am sure you can use canvas to get the base64 dataURL but I am sure it is not as fast as a string manipulation. Also I am not worried about converting an image into base64 but more interested in creating the image.