You would have to store the value in the database or somewhere else in the WebForms, request a reload using Update() and set the new color in BeforeEventRender event handler.
However, you can do it directly on the client side:
EventClickJavaScript="changeColor(e)"
<script type="text/javascript">
function changeColor(e) {
e.client.backColor("red");
dps.events.update(e);
}
</script>