Against all my expectations, the “variant” spelling, diahrroea, has a long history on both sides of the pond.
- The Thomsonian Recorder, Volume 2. Printed in Columbus (Ohio), in 1834

I have said that in almost every instance, Cholera is attended by diahrroea, of a peculiar character no doubt, because arising from a peculiar cause: nevertheless, easily manageable by an intelligent physician;
- Canine Pathology: Or a Description of the Diseases of Dogs. Third edition, printed in London, 1832.
When mercurial preparations are licked by dogs they are apt to occasion violent and dangerous diahrroea.
- Report on Epidemic Cholera and Yellow Fever in the Army of the United States, During The Year 1867

SIR: I have the honor to transmit herewith my monthly report of sick and wounded at this post during the month of June, 1867; also the special report upon epidemic cholera required by Circular No 3, dated Surgeon General's Office, April 20, 1867.
Although diahrroea and dysentery have been quite prevalent during the latter part of the month, but two cases of cholera have occurred.
- Royle's Manual of Materia Medica and Therapeutics Sixth Edition. Printed in London, 1876, written by John Harley, M.D.
HON. FELL. KING'S COLLEGE. ASSISTANT PHYSICIAN TO, AND LECTURER ON PHYSIOLOGY AT, ST THOMAS'S HOSPITAL

This is a warming stomachic tonic or aperient, useful in diahrroea or dyspepsia with flatulent colic.
Summary
Despite the evidence which suggests otherwise, the spelling variant diahrrœa or diahrroea is not recorded in any dictionary online. In Wiktionary, the (mis)spelling only occurs in a citation, in the entry for restrict
After suffering diahrroea, the patient was restricted to a diet of rice, cold meat, and yoghurt.
It also occurs in a Wikipedia discussion on Homeopathy, dated June, 2012. But on their page dedicated to the illness itself, Wikipedia lists only two spellings: Diarrhea, also spelled diarrhoea,