Exporting my custom content tables for a module I've been working on a Drupal 7 module. As I've been going along, I have been adding content types in the database through the Drupal 7 admin. 

I now want these content types to be created when my custom module is installed.

Rather than coding this manually in the module, is there any module available that can look at the content types on my site and create the code I need to put in the module install script?
You should look at the Features module. It will generate a module, which you can merge with your custom code.