You need to perform two step to get this working however I have checked this with version 1.8 but hope it will work in your case also
step 1. copy file app/code/core/mage/catalog/block/product/view/type/configurable.php
And create a folder under app/code/local with same directory structure mage/catalog/block/product/view/type/configurable.php
Now find function name getJsonConfig in configuration.php file.
Go to following code
$info['options'][] = array(
'id' => $value['value_index'],
'label' => $value['label'],
'price' => $configurablePrice,
'oldPrice' => $this->_prepareOldPrice($value['pricing_value'], $value['is_percent']),
'products' => $productsIndex,
);
Before this code place below two lines of code
$simpleproduct = Mage::getModel('catalog/product')->load($productsIndex);
$qty = (int)Mage::getModel('cataloginventory/stock_item')->loadByProduct($simpleproduct)->getQty();
Here you can see that i'm getting product stock by product id, now in info option array code you have to add one parameter
$info['options'][] = array(
'id' => $value['value_index'],
'label' => $value['label'],
'price' => $configurablePrice,
'oldPrice' => $this->_prepareOldPrice($value['pricing_value'], $value['is_percent']),
'products' => $productsIndex,
'qty' => $qty, // we are sending stock parameter so we can use it latter in drop down field
);
step 2. Now go js/varian/configuration.js
find the following line
if(allowedProducts.size()>0){
options[i].allowedProducts = allowedProducts;
element.options[index] = new Option(this.getOptionLabel(options[i], options[i].price), options[i].id);
Place following line under this
element.options[index].innerHTML += " Stock is :"+options[i].qty;
that's it all about cheer
Let me know if you have any query