This will do it.

Add the class "myDate" to your date field and copy in this JavaScript. 

I want to note that this is not my original code. A couple years ago, someone here helped me with code that would limit my datepicker to only Sunday, and all I've done here is tweak that a bit for you.

I hope this helps!

/*Limits date selection exclude weekends*/
$(document).ready(function(){
  function isCorrectDate(n) {
    var t = n.getDay();
    var d = n.getDate();
    return (t!=0 && t!=6);
  }
  function checkDate(n) {
    return[isCorrectDate(n),""];
  }
  function checkField(input, inst) {
    if ($(input).closest('li').hasClass('myDate')) {
      $(input).datepicker("option", {beforeShowDay: checkDate});
    }
  }
  $.datepicker.setDefaults( {beforeShow: checkField} );
  window.Parsley.addValidator('secondsat', {
    validateString: function(value) {
      return isCorrectDate(new Date(value));
    },
    messages: {
      en: 'Not valid date.'
    }
  });
  $('.myDate input').attr('data-parsley-secondsat','');

 });