I ended up using these methods to convert core data objects into JSON. To deserialize these objects I need to define a different class of mapping: RKManagedObjectMapping, which is slightly different from the regular object mapping.
-(void)setupObjectSerializationMapping
{
    RKObjectManager *objectManager = [RKObjectManager sharedManager ] ;
    RKObjectMapping *mapping = [RKObjectMapping mappingForClass:[Article class]];
    [mapping mapAttributes:@"articleID", @"title", @"body", nil];
    //********************************    
    RKObjectMapping *imageMapping = [RKObjectMapping mappingForClass:[EventImage class]];
    [imageMapping mapAttributes:@"createDate", @"localFilePath", nil];
    [objectManager.mappingProvider addObjectMapping:imageMapping];
    [objectManager.mappingProvider setSerializationMapping:[imageMapping inverseMapping] forClass:[EventImage class]];
    [objectManager.mappingProvider setMapping:imageMapping forKeyPath:@"eventImages"];
    //********************************    
    RKObjectMapping *eventMapping = [RKObjectMapping mappingForClass:[Event class]];
    [eventMapping mapAttributes:@"createDate", @"note", nil];
    [eventMapping mapRelationship:@"eventImages" withMapping:imageMapping];
    [objectManager.mappingProvider addObjectMapping:eventMapping];
    [objectManager.mappingProvider setSerializationMapping:[eventMapping inverseMapping] forClass:[Event class]];
    [objectManager.mappingProvider setMapping:eventMapping forKeyPath:@"events"];
    //******************************** 
    //setup App user mapping
    RKObjectMapping *userMapping = [RKObjectMapping mappingForClass:[AppUserSubclass class]];
    [userMapping mapAttributes:@"userID",@"firstName", @"lastName",@"localDataFilepath", nil];
    [userMapping mapRelationship:@"events" withMapping:eventMapping];
    [objectManager.mappingProvider addObjectMapping:userMapping];
    [objectManager.mappingProvider setSerializationMapping:[userMapping inverseMapping] forClass:[AppUserSubclass class]];
    [objectManager.mappingProvider setMapping:userMapping forKeyPath:@"appUser"];
}
-(NSString*)generateLocalJSONData
{
    NSString* folderPath = [self dataFolderPath];
    // remember what the file was called. This will not include the documents directory and will be the same on all machines.
    NSString* localFileName = [self fileName];
    NSString* dataFile = [self fullDocumentsFilePath];
    self.localDataFilepath = dataFile;
    NSAssert(self.localDataFilepath!=nil,@"failed to save local data path");
    //********************************
    NSError* error = nil;
    //app user subclass is the same as AppUser, but is used to differentiate between file based mapping and core data mapping
    RKObjectMapping *serMap = [[[RKObjectManager sharedManager] mappingProvider] serializationMappingForClass:[AppUserSubclass class]];
    NSDictionary *d = [[RKObjectSerializer serializerWithObject:self mapping:serMap] serializedObject:&error];
    if(error!=nil)
    {
        NSLog(@"!!!!! Error: %@",[error localizedDescription]);
    }
    NSString* dataContents = [d JSONString];
    BOOL success =  [dataContents writeToFile:dataFile atomically:YES encoding:NSUTF8StringEncoding error:nil];
    if(!success)
    {
        NSLog(@"Error writing to data file!");
    }
    [[AppUser managedObjectContext] save:nil];
    return dataFile;
}