How can a Part CAMO organisation, without having a contract with an operator, demonstrate the ability to manage Aircraft Maintenance Programmes (AMPs), when the figure of ‘generics’ in Part CAMO disappears?

The standard does not impose a "basic" or "generic" maintenance program; however, Chapter 1.2 of the CAME should describe how the organisation will develop the AMP. 
The organization must define the means to demonstrate that they are competent for the management that is intended to be carried out. Certain elements, such as the IT tool to manage the AMP, access to applicable technical documentation and/or staff experience in AMP matters, can contribute to achieving this objective.