To use the Happeo API with System Accounts, you will need to:

Create a system account
Create an api key for that system account
Give the correct user rights for the system account. The system account acts like a standard user in Happeo. This means for example adding admin rights to access user licensing, or adding the system account to a channel to let it post into it.

When this is done, you can then call the API with the api key passed into a header named 'x-happeo-apikey'.

...
Content-type: application/json
x-happeo-apikey: your-api-key
...