YOUR_TEMPLATE = name of your template
open includes/modules/YOUR_TEMPLATE/new_products.php
if it don't exist, create it. Copy from includes/modules/new_products.php
around line 72 find:
'text' => (($new_products->fields['products_image'] == '' and PRODUCTS_IMAGE_NO_IMAGE_STATUS == 0) ? '' : '<a href="' . zen_href_link(zen_get_info_page($new_products->fields['products_id']), 'cPath=' . $productsInCategory[$new_products->fields['products_id']] . '&products_id=' . $new_products->fields['products_id']) . '">' . zen_image(DIR_WS_IMAGES . $new_products->fields['products_image'], $new_products->fields['products_name'], IMAGE_PRODUCT_NEW_WIDTH, IMAGE_PRODUCT_NEW_HEIGHT) . '</a><br />') . '<a href="' . zen_href_link(zen_get_info_page($new_products->fields['products_id']), 'cPath=' . $productsInCategory[$new_products->fields['products_id']] . '&products_id=' . $new_products->fields['products_id']) . '">' . $new_products->fields['products_name'] . '</a><br />' . $products_price);
this is where you would add your code to put in a buy now button. I would suggest looking at the code in the includes/modules/product_listing.php file for reference. Simply change all instances of $product_listing to $new_products