Tinywatermark is cloning the original input and replacing it with that clone. Thats why dateinput isn't working there any more. You can try to use something like this:
$('input')
.datepicker()
.on('blur', function() {
if ($(this).val() == '') {
$(this).val('choose date');
}
})
.on('focus', function() {
if ($(this).val() == 'choose date') {
$(this).val('');
}
})
.trigger('blur');