Cart Attributes: datepicker https://docs.shopify.com/themes/customization/cart/add-date-picker-for-delivery-dates

delivery-date.liquid

{{ '//code.jquery.com/ui/1.9.2/themes/base/jquery-ui.css' | stylesheet_tag }}
{{ '//ajax.googleapis.com/ajax/libs/jqueryui/1.9.2/jquery-ui.min.js' | script_tag }}

<div style="width:300px; clear:both;">
  <p>
    <label for="date">Pick a delivery date:</label>
    <input id="date" type="text" name="attributes[date]" value="{{ cart.attributes.date }}" />
    <span style="display:block" class="instructions"> We do not deliver during the week-end.</span>
  </p>
</div>

<script>
jQuery(function() {
  jQuery("#date").datepicker( { 
    minDate: +1, 
    maxDate: '+2M',
    beforeShowDay: jQuery.datepicker.noWeekends
  } );
});
</script>

{% comment %}
  To remove days of the week that aren't Saturday and Sunday, use this:
  http://stackoverflow.com/questions/2968414/disable-specific-days-of-the-week-on-jquery-ui-datepicker
{% endcomment %}