MySQL query and array output from same database column

You can change your sql to get the meta_key field as well:

SELECT wp_posts.ID,
    wp_postmeta.meta_value,
    wp_postmeta.meta_key
FROM wp_posts
    INNER JOIN wp_postmeta
       ON wp_posts.ID = wp_postmeta.post_id
WHERE wp_posts.post_type = 'cooney_properties'
AND wp_posts.post_status = 'publish'
AND (wp_postmeta.meta_key = 'longitude' OR wp_postmeta.meta_key = 'latitude')

Then you can iterate the returned array, and populate a new one using the ID values as the index. You can check if an item with the current id exists in the new array, with isset(). If so, add to it (eg add the latitude value) else create the item:

$new=array();

foreach($result as $item){

    if(isset($new[$item->ID])){

        $new[$item->ID][$item->meta_key] = $item->meta_value;

    }else{

        $new[$item->ID] = array('ID' => $item->ID, $item->meta_key => $item->meta_value);
    }
}
print_r($new);

I think that first of all you have to add in your query a "type" value that indicates if a meta_value is "longitude" o "latitude":

SELECT wp_posts.ID,
    wp_postmeta.meta_value,
    wp_postmeta.meta_key as type
FROM wp_posts 
    INNER JOIN wp_postmeta
       ON wp_posts.ID = wp_postmeta.post_id
WHERE wp_posts.post_type = 'cooney_properties'
AND wp_posts.post_status = 'publish'
AND (wp_postmeta.meta_key = 'longitude' OR wp_postmeta.meta_key = 'latitude')

In this way, your autoput array will be like this:

Array
    (
     [0] => stdClass Object
    (
        [ID] => 25016273
        [meta_value] => 51.01454
        [type] => 'longitude'

    )
     [1] => stdClass Object
    (
        [ID] => 24617570
        [meta_value] => 51.01447
        [type] => 'longitude'
    )
     [2] => stdClass Object
    (
        [ID] => 24780750
        [meta_value] => 51.01535
        [type] => 'longitude'
    )

     ------------------- (later on items with same ID) -------------

     [141] => stdClass Object
    (
        [ID] => 24617570
        [meta_value] => -3.107139
        [type] => 'latitude'
    )
     [142] => stdClass Object
    (
        [ID] => 24780750
        [meta_value] => -3.096807
        [type] => 'latitude'
    )
     [143] => stdClass Object
    (
        [ID] => 24764956
        [meta_value] => -3.104187
        [type] => 'latitude'
    )

Then you can use a cyle to popolate an array, using particula conditions:

$result = array();
foreach(your_array AS $k => $v) {
  $result[$v->id][$v->type] = $v->meta_value;
}

At this point you have an array like this:

array(
  [25016273] = array(
    ['longitude'] => 51.01454,
    ['latitude'] => -3.104187
  ),
  [24617570] = array(
    ['longitude'] => 51.01454,
    ['latitude'] => -3.104187
  )
  ....
)

If you want exactly the output structure that you indicate in you question, you can iterate on this array to obtain what you want:

$result = array()
$i = 0
foreach ($new_array as $k => $v) {
  result[$i]->id = $k;
  if (isset($v['longitude']) result[$i]->longitude = $v['longitude'];
  if (isset($v['latitude'])result[$i]->latitude = $v['latitude'];
  $i++;
}