You could use :nth-of-type(n)
to override the previous pseudo classe styles like this :
.secondary-slider .ui-state-default:nth-of-type(n) {
background: url('single-point-arrow.png');
}
OR
You can make the second CSS style more specific as you have two calsses on your container, you can use both like this :
.base-slider.secondary-slider .ui-state-default {
background: url('single-point-arrow.png');
}