You cannot tell the default class pickler to ignore something, no.
jsonpickle does support the pickle module __getstate__ and __setstate__ methods. If your classes implement those two methods, whatever is returned is then used by jsonpickle to represent the state instead. Both methods do need to be implemented.
If __getstate__ is not implemented, jsonpickle uses the __dict__ attribute instead, so your own version merely needs to use that same dictionary, remove the _sa_instance_state key and you are done:
def __getstate__(self):
state = self.__dict__.copy()
del state['_sa_instance_state']
return state
def __setstate__(self, state):
self.__dict__.update(state)
Whatever __getstate__ returns will be processed further, recursively, there is no need to worry about handling subobjects there.
If adding __getstate__ and __setstate__ is not an option, you can also register a custom serialization handler for your class; the disadvantage is that while __getstate__ can get away with just returning a dictionary, a custom handler will need to return a fully flattened value.