The main meaning of happy-clappy, when used as an adjective, is: belonging to, or characteristic of, a Christian charismatic or evangelical group whose worship is marked by enthusiastic participation; as a noun, the word denotes a member of such a Christian group.
With allusion to the cheerful singing and hand-clapping regarded as typical of charismatic religious services, this word is composed of the adjective happy and of the noun clap suffixed with -y.
(Here, charismatic, as in charismatic renewal, designates a movement within certain Western Churches to restore the charismata or spiritual gifts (especially speaking in tongues and prophecy) to a central place in the life and worship of the Church.)
The earliest instance of happy-clappy, used in this sense, that I have found is from the very beginning of the review of Dr J. I. Packer’s book Keep in Step with the Spirit, published in The Age (Melbourne, Victoria) on 1st April 1985:
Two brands of Christianism making themselves felt today are the “born again” kind professed by Jimmy Carter and supportive of Ronald Reagan, and the happy-clappy, tongues-speaking, faith-healing kind called Pentecostal until it invaded the mainline churches in the late 1960s and became “charismatic renewal”.
In Sweet singing in the choir, published in The Observer (London) on 22nd December 1985, Janet Walks “investigates the strange British phenomenon of choirboys and choir schools”; she evokes the threat that the evangelical and charismatic wing of the Church, which encourages congregational participation, poses to the choral tradition; however, she writes, the Rev. John Reed, precentor of St Albans Cathedral, has found an inclusive approach:
John Reed at St Albans admits that he sympathises with both sides. ‘To me, variety is the spice of faith as well as of life. On some Sundays we have happy-clappy sessions here with choruses and flute and guitars for our parish communion; later the same morning we would have a high-swung mass with incense and the choir singing a setting by Palaestrina or Schubert or Byrd.’
The earliest noun-use of happy-clappy that I have found is from A different kind of heavenly body works out at this gym, by Jenny Chater, published in The Northern Herald section of The Sydney Morning Herald (Sydney, New South Wales) of 14th April 1988:
Malcolm Thompson is not your usual kind of pastor. He doesn’t wear a dog collar or robes. When he is not preaching, he is often out surfing. He used to be a drug-user. And he preaches in a fitness centre.
“I believe church should be fun, with a capital F-U-N,” he says.
His pentecostal [sic] services are full of dancing and up-beat singing, with music from an electric rock band – which is why Pentecostals are nicknamed “happy clappies”. They hold concerts, featuring Christian bands with names like Aliens In Exile.
Pastor Malcolm Thompson with his wife, Jane, at the church in the gymnasium.
However, the word has been used with other meanings; on 16th June 1958, The Asheville Citizen (Asheville, North Carolina) evoked
the soothing strains of a string band and the happy-clappy feet of nimble square dancers.
And the scathing review of an Italian restaurant called The Olive Garden, published in The Pantagraph (Bloomington, Illinois) on 14th December 1990, mentioned
those happy-clappy waiters and waitresses who seem to love to sing birthday cheer, but appear to know next to nothing about the menu.
(This reviewer used the image of birthdays raucously celebrated by “happy-clappy” waiters and waitresses on several other occasions during the 1990s.)