The situation is that the ballad tune specified, namely Coming Down has been lost.

Simpson treats the tune Coming Down (specified for the Captain Kid... song) under the heading song Sound a Charge and here is most of the text for that tune:

I have not found a ballad from which the tune name "Sound a Charge" could be derived. About 1660, however, a ballad was published that calls for the tune. It is T.R.'s "The Royall Subjects Joy" (Euing, Roxburghe; reprinted in RB VII 678), which has the following distinctive stanza form:

  You Loyall Subjects all
    sing for joy, sing for joy
  Good news here's at White-Hall,
    sing for joy,
  A second Charles is come,
  Though heavy news to some,
  Let them say no more but mum,
    sing for joy, sing for joy.

Another is "Touch and go; or, The French Taylor finely Trapann'd", c1670, beginning " A Tayler in the Strand,/Touch and go, touch and go," to the tune "Sound a Charge, Sound a Charge" (Rawlinson, reprinted in RB VII, 486). Its stanza contains four rather than three lines upon the b rhyme.

I have found no music entitled "Sound a Charge". The Dancing Master, 1701 et seq., contains a tune "Touch and Go", whose rhythms are unsatisfactory for singing either ballad. Several other pieces cast in the mold of "The Royall Subjects Joy" give us names of still other tunes which do not seem to have survived: "Captain Kid's Farewell to the Seas," c.1701, is to the tune of "Coming Down" (Lord Crawford 843, reprinted in C.H.Firth's Naval Songs and Ballads, 1908, p134); and a D'Urfey poem "The Moderator's Dream" is to "Chimney Sweep" (Pills, 1719-1720, II, 182, without music). There is however in Pills, 1714, V, 117, VI 251, an amorous song beginning "A Young Man and a Maid, put in all, put in all" which contains music (Fig 438) suitable to all these ballads save the hpermetrical "Touch and Go". The same air is found in The Dancing Master, II, 2d ed, 1714, 121, entitled "Put in All". Although we cannot be sure that this tune was used for the seventeenth century pieces, a strange bit of evidence strengthens the possibility. "Londons Farewell to ye parliament," a manuscript ballad of c.1642 in the hands of Henry Lawes and attributed to him, is coupled with an unnamed air (Fig 439) clearly related to the eighteenth-century "Put in all". The first stanza, a variant form interlining the music, shows the close metrical similarity to the ballads just cited:

  farewell to ye parlyament
    with a Hey with a Hey
  far well to ye parliament
    with a Hoe,
  your dear delight ye Cittye,
  whose wants have made us witty
  & a figg for ye close Comittee
    with a Hey tronony nony noe

Except for the length of the closing line here (in the text of the ballad the line contains an additional "nony") the structure is congruent with that of the other pieces under discussion. The difference is reflected in the final phrases of the two tune ....

The stanza pattern of "The Royall Subjects Joy" is also found in the more recent ballad "Sam Hall," with a fine traditional tune. It lies, however, outside the scope of our discussion. (Footnote: For an illuminating study of the roots of this ballad and associated texts and tunes, see Bertrand H. Bronson "Samuel Hall's Family Tree," California Folklore, I (1942), 47-64)

(I'll put up the two tunes later, but my dog is currently demanding the great outdoors!)

So Coming Down is lost, though the tune given by Simpson from Pills could be used (parts are similar to the Captain Kidd tune you know, though minor) or you could use something from the Sam Hall family.

Mick