Basically the glyphicon icons are fonts and you can change the color of them just with the css color property. So, changing the color of the font, you will change the background. Now, fonts have no border-color property, but you can simulate it using text-shadow

.glyphicon{
    font-size: 60px;
    color:red;
    text-shadow: -2px 0 black, 0 2px black, 2px 0 black, 0 -2px black;
}

http://jsfiddle.net/9suc171t/1/