My name is Caleb and I am a member of Constant Contact's API Developer Support Team.
Due to the design of our automated series only being capable of creating GUI campaigns paired with our API only being capable of creating custom coded campaigns prevents us from being capable of opening an endpoint for the creation of automated series through the API. That being said, you are able to trigger a pre-existing list-join automated series by adding contacts through the API into the associated mailing list for the series. This does require that you set the series up within the account, however it is the only method that will allow for the API to interact with the series.
Create an Automated Series: