Adrock.use the below for more suitable solution
$model = Mage::getModel('facebook/facebookcoupon') ->getCollection()
->addFieldToFilter('facebook_id', 14547854) ->getFirstItem();
// here you'll get a collection but single record -
Please note:
loadByField($field,$value) in resource model is wrong.you can use load()
function only whenever,you will be trying to fetch data using primary key.