On the page where the search box is used, add the following style sheet.  As a template it changes various aspects of the dropdown style – modify as desired.  Note that the “!important” modifier is used to specify that it should override any default styling specified by the controls.

<style type="text/css">

        /* container box */

        .sew_ac_results {

               border-color: blue !important;

               background-color: #ededed !important;

        }

        /* suggestion text span */

        .sew_suggestion

        {           

               color: Red !important;

        }

        /* suggestion number of results span */

        .sew_results

        {

            color: blue !important;

        }

        /* suggestion highlighting */

        .sew_ac_over, .sew_ac_over .sew_suggestion, .sew_ac_over .sew_results {

               background-color: Highlight;

               color: white !important; /*HighlightText*/

        }

</style>