Developing an Android device
While there isn't a simple solution to the stated requirement, here is one approach:


Purchase, in retail, a new cheap Android phone that meets the specifications. Often the "old cheap" phones will be more expensive than new models, and will also suffer from spares (batteries!) sourcing. 
Also purchase an Android Accessory Development Kit (ADK), either the official Arduino ADK, or one of the many clones and ADK compatible development boards ($49 on eBay) out there.

Integrate the barcode reader into the ADK board - The ADK is a USB host, so USB devices can be connected to it.


Once you have a working prototype through the steps above, either integrate all the constituent parts into a single board that integrates with a generic Android phone, or find a suitable electronics design business that will do this for you.