First you need to create your carousel module.
While adding or editing module you do not have to select pre-defined module positions. Module positions that you can select are defined in template so it can be displayed on whichever page or homepage when you are using the templates positions. But we are not limited to modules positions that have already being defined by template, by writing your module position yourself into text-box you are simply defining new module position which you can use inside articles with "Content Load Modules" plugin.
See following image.
Adding new position "mynewmoduleposition".
Lets say for this example we use K2 item numbers for our module name as you will be using a lot of modules it is easier to remember them by k2 item id.
K2 item id = 200
Module named: 200
Custom position entered: 200
Syntax to load inside an article or K2 article would be : {loadposition 200}
Make sure Plugins > Content Load Module Plugin is enabled. Also in K2 settings make sure plugins are enabled.
See you around...