The cloth that covers the coach-box, in which hammer, nails, bolts, etc., used to be carried in case of accident. Another etymology is from the Icelandic hamr (a skin), skin being used for the purpose. A third suggestion is that the word hammer is a corruption of “hammock,” the seat which the cloth covers being formed of straps or webbing stretched between two crutches like a sailor's hammock. Still another conjecture is that the word is a corruption of “hamper cloth,” the hamper being used for sundry articles required, and forming the coachman's box. The word box seems to favour this suggestion.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894