JSFiddle - React, Tailwind, and code Playground

HTML

<select multiple="multiple" id="carros" size="1" name="carros">
    <option value="volvo">Volvo</option>
    <option value="saab">Saab</option>
    <option value="opel">Opel</option>
    <option value="audi">Audi</option>
</select>
<img id="up" src="http://www.tacoma.washington.edu/graphics/arrow_up_black.gif"/>
<img id="down" src="http://as-se.awr.org/images/templates/global/listen/program/black-down-arrow.gif?1343273297"/>

CSS

select {
    height: 20px;
}

JavaScript

$('#up').click(function() {
    $('select').scrollTop($('select').scrollTop() - 10);
});
$('#down').click(function() {
    $('select').scrollTop($('select').scrollTop() + 20);
});