Black ones containing family’s swimwear (6)
I believe the answer is:
Here is my best explanation:
'swimwear' is the definition.
(I've seen this before)
'black ones containing family's' is the subsidiary indication.
'black' becomes 'b' (as in pencil classifications).
'ones' becomes 'ii' (I can't justify this - if you can you should believe this answer much more).
'containing' is an insertion indicator.
'family' becomes 'kin' ('kin' can be a synonym of 'family').
'ii' placed around 'kin' is 'ikini'.
(Other definitions for bikini that I've seen before include "Brief bathing costume", "Tiny bathing costume", "skimpy costume", "Small two-piece bathing suit", "Skimpy bathing costume or Pacific atoll", "tests were carried out here", "Atoll and swimming costume", "Brief two-piece swimming costume", "Clothing to wear on the Pacific atoll?" and "A-test atoll - type of wax?".)