This is largely a matter for speculation, but I would argue that the title of the play refers to its subversion of the rural idyll. Just as pretty flowers often bring on the unpleasant symptoms of the medical condition of the same name, so the idyllic rural retreat of the Bliss family induces a similarly uncomfortable feeling among their unfortunate guests.

One often thinks of the countryside as a place of peace and quiet, of rest and repose. But not for the guests who rock up at the Bliss family's Thames-side retreat. They are subjected to all manner of indignities during their stay such as cruel parlor games, bad food, and beds that wouldn't look out of place in a torture chamber. Like a beautiful golden sunflower that harbors a deadly hit of pollen for the unwary hay fever sufferer, the Bliss' outwardly stunning country retreat conceals something nasty, unpleasant, and supremely irritating.

I looked for a definitive quote from Noel Coward, but couldn't find one.  My best guess is that it is just a clever word play.  "Hay Fever" as an allergy typically associated with springtime; springtime of course, is associated with "blooming" of both plants and lovers.  Both literally and psychically then, "hay fever" can make a person act outside his normal comfort level, trying to find relief, to scratch an itch, as it were...

Here is a brief overview of the play:

Regarded by many as Noel Coward's funniest play, it concerns the ultra-Bohemian Bliss family. Mother Judith is a retired dramatic actress; father David, a successful but temperamental writer; and their adult son and daughter, who are handsome and ill-mannered. One weekend, each has invited a guest to their country home without the knowledge of the other family members. What ensues is a wild romp as each person is attracted to someone different from the original pairings. Light, luminous, charming and hilarious.