After writing up and posting everything below the double lines, I found this.
From Langensheidt's Pocket Merriam-Webster, Dictionary of Synonyms and Antonyms, 1998 Google Books (snippet)
1. Bending; capable of being bent or folded with ease; supple, lithe, flexible
from the 14th century onward
Antonyms of pliant from Thesaurus.com, Merriam-Webster.com, Synonyms.com and a number of other common thesaurus sites offered:
stiff, rigid, inflexible, intractable, unadaptable and a few others.
Not one of the common thesaurus sites offered the most obvious antonym of pliant which is unpliant
1 Not bending readily or easily; stiff.
from the 17th century onward
The un- prefix expresses negation, but so does the im- prefix, particularly before the letters b, m and p and there's no doubt that pliant starts with p.
So why is impliant not in any dictionaries (apart from Burton's Legal Thesaurus 4th Ed. which only mentions it as a synonym of unyielding but in the 5th Ed. it gets it's own mention with unyielding as it's synonym)?
It's hard to tell really, there's plenty of usage for impliant to be found in Google Books (mostly 18th century but some modern ones too).
London Magazine, Vol.24, 1755 in a section about 'Observations on grafting' Google Books
...either in the wood already formed, and which then ceases to be supple, or in the gross bark, which is altogether as impliant as the wood.
Lectures to working men, Rev. Arthur Mursell, 1859 Google Books
The stubborn clay which was tough and impliant in the woman's hands, may be moulded at pleasure by the fingers of the child.
The John Dewey Society Lectureship Series, v5, 1962 Google Books (snippet)
... sculptors who left even upon such impliant clay as mine the delicate chiseling of refined genius, ...
Cruise Control, Victoria Jenkins, 2002 Google Books (snippet)
A couple of glasses of late harvest chardonnay to help dissolve the unacceptable impliant crust of the banana-peach tart ...
While I was looking for these uses of impliant one thing became quite clear, impliant appears in a number of French-to-English dictionaries so perhaps it was always thought of as a French word that was trying to become assimilated into English but never quite made it, because we already have unpliant. I am genuinely surprised, given the number of uses impliant has had in the last half millenium that it's not listed in the OED at all, not even as erroneous or rare.
All in all, impliant is a perfectly good word that obviously means not pliant, however the more common term is unpliant. The surprising thing about unpliant is that I have not found a single reference that mentions it as an antonym of pliant.