We will use "CSS Pseudo-classes" to achieve it. The hardest thing here is that we should handle displaying icons in different cases. There is a case both "arrow up" and "arrow down" showing and other case is only one of these icons is shown.
.ui-sortable-column-icon.ui-icon.ui-icon-carat-2-n-s {
    background-image: none;
    margin-left: 5px;
    font-size: 1.1666em;
    position: relative;
}
.ui-sortable-column-icon.ui-icon.ui-icon-carat-2-n-s:not(.ui-icon-triangle-1-s)::before {
    content: "\f106";
    font-family: "FontAwesome";
    position: absolute;
    top: -2px;
    color: rgba(0,0,0,0.4);
}
.ui-sortable-column-icon.ui-icon.ui-icon-carat-2-n-s:not(.ui-icon-triangle-1-n)::after {
    content: "\f107";
    font-family: "FontAwesome";
    position: absolute;
    top: 5px;
    color: rgba(0,0,0,1);
}
.ui-sortable-column-icon.ui-icon.ui-icon-carat-2-n-s.ui-icon-triangle-1-n::before {
    color: rgba(0,0,0,1);
}
Hope it useful when you get the same issue. ;)
 
