You may use this, if you’re unafraid of employing an unusual word, to refer to a person who rarely or never laughs (the related noun is agelast, a person who never laughs).
The Oxford English Dictionary not only marks this as obsolete, but finds only two examples, from seventeenth and eighteenth century dictionaries. Searching the literature proves the word’s not that rare, though most of its modern appearances are in scholarly or literary contexts.
Umberto Eco's novel The Name of the Rose (“spaghetti structuralism” according to Slavoj Ciuek, but fun all the same) dramatised the disappearance of the last surviving copy: literally eaten as a subversive tract by a gloomy “agelastic” monk, before his whole monastery goes up in flames.
Guardian, 25 Sep. 2010.
Its modern recrudescence may have been provoked through its use by George Meredith in An Essay on Comedy of 1877: “It is but one step from being agelastic to misogelastic” (miso- means hatred of something, as in misogyny, the hatred of women), though nearly all the examples that I can find are in works of the 1990s onwards. Walter Redfern uses it in his book French Laughter: Literary Humour from Diderot to Tournier (2008): “Is not sex spasmodically but regularly comic, for everyone except the most mechanical, brutal, and agelastic performers?”
Its opposite, gelastic, is more common and hasn’t suffered the vicissitudes of fortune of its negative partner. You will come across this most often in medical terminology, principally in gelastic seizure, a form of epilepsy in which bursts of pathological laughter are a symptom. Somebody hypergelastic laughs a lot.
All three words derive ultimately from Greek gelos, laughter.