Hi Rholzler,
I had the same issue with all my j-cook components under 3.7 (php7.0).
But it's not a j-cook Issue, but a Joomla3.7 CSS issue. The class name has changed, and will be corrected in next release.
In
root/libraries/cms/html/behaviour.php => just add a '-' after calendar, :
JHtml::_('stylesheet', 'system/calendar-jos.css', array('version' => 'auto', 'relative' => true), $attribs);
JHtml::_('script', $tag . '/calendar-setup.js', array('version' => 'auto', 'relative' => true));
and j-cook calendar will work