When we create a custom post type with can_export set to true, we can export the custom post types from the admin export screen. When the CPT is selected, the export creates a WXR file with all of the posts of this type. We can add filters to the custom post type so that a subset can be exported.

First add the HTML markup required using the javascript.

function reviews_export_js() {
?>
<script type="text/javascript">
//<![CDATA[
  jQuery(document).ready(function($){
    var form = $('#export-filters');
        ourradio = form.find('input:radio[value=reviews]');
        ourradio.closest('p').after('<ul class="u-export-filters" id="reviews-filters" style="margin-left: 18px; display: none;">\n<li>\n<label>Date range:</label>\n<?php date_filter(); ?> </li>\n</ul>\n');
      filters = form.find('.export-filters');
    form.find('input:radio').change(function() {
      switch ( $(this).val() ) {
        case 'reviews': $('#reviews-filters').slideDown(); break;
        default: $('#reviews-filters').slideUp(); break;
      }
    });
  });
//]]>
</script>
<?php
}
add_action( 'admin_head-export.php', 'reviews_export_js' );

We are using admin_head-export.php action hook. This is called whenever the export screen is loaded. The method review_export_js adds the necessary markup. We first find the radio button displaying our custom post type and then append the required filter markup. In this case we are adding a date filter to the custom post type. The date_filter method just echos the markup for the starting and ending dates.

function date_filter() {
    s_date_filter();
    e_date_filter();
}

function s_date_filter() {
  echo '<select name="reviews_start_date">';
  echo '<option value="0">' . __( "Start Date" ) . '</option>';

  reviews_export_date_options();
  
  echo '</select>';
}

function e_date_filter() {
  echo '<select name="reviews_end_date">';
  echo '<option value="0">' . __( "End Date" ) . '</option>';

  reviews_export_date_options();
  
  echo '</select>';
}

function reviews_export_date_options() {
  global $wpdb, $wp_locale;

  $months = $wpdb->get_results( "
    SELECT DISTINCT YEAR( post_date ) AS year, MONTH( post_date ) AS month
    FROM $wpdb->posts
    WHERE post_type = 'reviews' AND post_status != 'auto-draft'
    ORDER BY post_date DESC
  " );

  $month_count = count( $months );
  if ( !$month_count || ( 1 == $month_count && 0 == $months[0]->month ) )
    return;

  foreach ( $months as $date ) {
    if ( 0 == $date->year )
      continue;

    $month = zeroise( $date->month, 2 );
    echo '<option value="' . $date->year . '-' . $month . '">' . $wp_locale->get_month( $month ) . ' ' . $date->year . '</option>';
  }
}

From now on, the export screen has the option of accepting the start date and end date fields whenever the custom post type is selected. Finally, we need to filter the records. We use the query filter to add the additional where clauses. But first, we ensure that we add the query filter only when export is taking place using the export_wp action hook.

function reviews_add_query_filter() {
  if( $_REQUEST['content'] == 'reviews')
    add_filter( 'query', 'reviews_query' );
}
add_action( 'export_wp', 'reviews_add_query_filter' );

The reviews_query method updates the query to include the filters for the start and end dates.

function reviews_query( $query ) {
  $args = array( 'start_date' => false, 'end_date' => false );
  if ( $_REQUEST['reviews_start_date'] || $_REQUEST['reviews_end_date'] ) {
      $args['start_date'] = $_REQUEST['reviews_start_date'] ;
      $args['end_date'] = $_REQUEST['reviews_end_date'] ;
  }

  global $wpdb;

  if ( $args['start_date'] )
      $query .= $wpdb->prepare( " AND {$wpdb->posts}.post_date >= %s", date( 'Y-m-d', strtotime($args['start_date']) ) );

  if ( $args['end_date'] )
      $query .= $wpdb->prepare( " AND {$wpdb->posts}.post_date < %s", date( 'Y-m-d', strtotime('+1 month', strtotime($args['end_date'])) ) );

  var_export($query);
  return $query;
}

You can adjust the reviews_query and date_filter methods to accept different filter conditions for export.