Inventory Management System for Website: Syncing to Quickbooks Premiere 2013?

Hi everyone,
Our client is running a book store with lots of inventory. They have been running the business for a few years and realize that the website sales (custom built CMS from scratch) does not sync to their localized QuickBooks inventory. Selling something online means printing the order out and manually adjusting the inventory in Quickbooks. As you can tell, this takes up a lot of time.

Is there a solution out there that will fix this for them? I have been looking at “ACCTivate” for Quickbooks but I don’t know if it only works with the eCommerce solutions they have mentioned below:

In other words, is it posible to sync our custom CMS generated sales to Quickbooks Premiere 2013? And if so, how deep can this go? Can we inform users if an item is currently out of stock? Is the syncing to be done automatically between the website and Quickbooks or will it need to be done with a manual import / export process?

We would really appreciate the help and feedback here.

Thanks!

PS. Also, the reason that they are going with QuickBooks (and have also upgraded to the newest version) is because the accounting department requires this software for year end tracking and all sorts of other important tax related things too. We were looking at building our own custom IMS but then realized for all of the features that QuickBooks offers it would take years to replicate just the ones that we need for accounting alone. I am hoping that something like ACCTivate will solve our needs for seamlessly working with QuickBooks but I am not crossing my fingers either…