You can set an Id to the link tag and switch the css at runtime.
HTML
<link type="text/css" rel="stylesheet" media="all" href="../green.css" id="theme_css" />
JS
document.getElementById('buttonID').onclick = function () {
document.getElementById('theme_css').href="https://stackoverflow.com/questions/red.css";
};
Quick Demo:
$( "#datepicker" ).datepicker();
$('button').button().on('click', function () {
let linkHref="https://code.jquery.com/ui/1.11.4/themes/{THEME}/jquery-ui.css";
if ($('#swapTheme').prop('href').indexOf('pepper-grinder') >= 0) {
$('#swapTheme').prop('href', linkHref.replace('{THEME}', 'black-tie'));
} else {
$('#swapTheme').prop('href', linkHref.replace('{THEME}', 'pepper-grinder'));
}
});
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<script src="https://code.jquery.com/ui/1.12.1/jquery-ui.min.js" integrity="sha256-VazP97ZCwtekAsvgPBSUwPFKdrwD3unUfSGVYrahUqU="
crossorigin="anonymous"></script>
<link href="https://code.jquery.com/ui/1.11.4/themes/pepper-grinder/jquery-ui.css" id="swapTheme" rel="stylesheet">
<div id="datepicker"></div>
<button style="padding: 5px 15px;"> Switch Theme </button>