User is not able to add product into wishlist in Magento

All the code you need can be found in app/code/core/Mage/Wishlist/controllers/IndexController.php method _addItemToWishList.
You will need to load the product by it's ID and load the wish list by customer. The code would look roughly something like this.



<?php

$wishlist = Mage::getModel('wishlist/wishlist')->loadByCustomer($customerId, true);
$product = Mage::getModel('catalog/product')->load($productId);

$buyRequest = new Varien_Object(array()); // any possible options that are configurable and you want to save with the product

$result = $wishlist->addNewItem($product, $buyRequest);
$wishlist->save(); ?>

Just out of curiosity. Why not use the addAction provided by the wishlist controller to add the products?
You can obtain the url via echo Mage::helper('wishlist')->getAddUrl($product);