Is it appropriate to wish a person Happy Yom Kippur?
Interesting question. The Mishnah (end of Taanis) actually writes that the day of Yom Kippur is the most joyful day of the year, which will apparently make the “happy” greeting appropriate.
However, in truth the greeting does not really match the spirit of the day, which is a grave — though certainly not say — day of fasting and atonement.
On account of this spirit the Sages write that Hallel, the customary song of joy for festival days, is not recited on Yom Kippur, and wishing somebody a meaningful Yom Kippur, or a Gemar Chasima Tova, is therefore more fitting.