As noted before, the 'original' (meaning earliest known in print)version of this secular game song is posted in the DT. A note should be added that it appeared in a toy-book by E. Pearson, c. 1780, a copy at the South Kensington Museum. (See Lina Eckelstein, 1906, "Comparative Studies of Nursery Rhymes," p. 74. (On Line)

Another early version is the one collected by Baring Gould from his aunt Cecily, 'about 1840.' The succession is:

The first day of Christmas my true love sent to me,
A part of a juniper tree
Two turtle doves etc.
Three French hens
Four colly-birds
Five, a golden ring
Six geese a-laying
Seven swans a-swimming
Eight hares a-running
Nine ladies dancing
Ten lords a-playing
Eleven bears a-baiting
Twelve bulls a-roaring.

Note- Only one golden ring at Five. The last two, baiting bears and bulls, is suppressed in present-day UK.
Sabine Baring Gould, 1889, Folk Songs of the West;" Twelfth Night Game of Forfeits. Sheet music reproduced in "The Hymns and Carols of Christmas":
www.hymnsandcarolsofchristmas.com/Hymns_and_Carols/twelve_days_of_christmas-1.htm

Also in J. O. Halliwell, 1842 (1846 4th ed.), "The Nursery Rhymes of England," pp. 121-123. (on line)

CCL
The First day of Christmas
My mother sent to me
A partridge in a pear-tree.

The second day of Christmas
My mother sent to me
Two turtle doves, etc.
Three French hens
Four canary birds
Five gold rings
Six geese a-laying
Seven swans a-swimming
Eight ladies dancing
Nine lords a-leaping
Ten ships a-sailing
Eleven ladies spinning
Twelve bells ringing.

"Each child in succession repeats the gifts of the day, and forfeits for each mistake. The accumulative process is a favorite with children; in early writers, such as Homer, the repetition of messages, etc., pleases on the same principle."

These may have been posted before, but I think it worthwhile to have them together.
I do not have the version of Edward F. Rimbault, 1864.