In contact form7 back end side dtaetime form tag is button appear. Suppose this tag button does not appear then please use contact7 Version 4.4.1 and contact form date picker Version 2.5.2.
Where is your date picker?
I have same problems on WP4.5 version.
I fixed this solution, please call Jquery latest library on wp_footer(); function in footer.php file.
Example like
<script src=”http://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js”></script>
<?php wp_footer(); ?>
