New coordinate systems can easily be added by users by simply subclassing the SphericalCoordinatesBase object. Detailed instructions for subclassing are in the docstrings for that class. If defining a latitude/longitude style of coordinate system, the _initialize_latlong method and _init_docstring_param_templ attribute are helpful for automated processing of the inputs.
To define transformations to and from this coordinate, the easiest method is to define a function that accepts an object in one coordinate system and returns the other. Decorate this function with transform_function function decorator, supplying the information to determine which coordinates the function transforms to or from. This will register the transformation, allowing any other coordinate object to use this converter. You can also use the static_transform_matrix and dynamic_transform_matrix decorators to specify the transformation in terms of 3 x 3 cartesian coordinate transformation matrices (typically rotations).