If I understand your question correctly, you can do the following:
- Identify the template being used to output your custom posts (or create one)
- Within this template, intercept the $_GET variable for date, sanitise it and parse it into a date that you can use in your posts query.
- Query the items (if you’re using the post date for date, you can use that; otherwise you can use a meta query to query on a meta value if you’re doing it that way).
Along the lines of
$day = date('d',strtotime($_GET['date']));
$month = date('m',strtotime($_GET['date']));
$year = date('Y',strtotime($_GET['date']));
$args = array(
'posts_per_page' => -1,
'year' => $year,
'monthnum' => $month,
'day' => $day,
'post_type' => my_post_type,
'order' => 'ASC',
'orderby' => 'post_date',
);
$myitems = get_posts($args);