'composition writing' is correct and usable in written English.
You can use it when you are referring to the process of creating a written piece, such as an essay or article. For example, "I find composition writing to be a creative and enjoyable process."
In the past decade he has returned to composition, writing eclectic works for voices and orchestra.
And here he is on the process of composition: "Writing music isn't really writing, it's designing".
He has also dabbled in composition, writing theme music for several of the TV shows he produces.
Along the way, he adopted an eccentric method of composition — writing for a live audience, as it were — to circumvent what he calls "the processes of my consciousness which are not well adapted to constructive behavior".
The Icelandic singer-songweriter Valgeir Sigurdsson works with electronics and a world-weary voice; the Canadian singer-songwriter Sandro Perri uses real instruments, no electronics at all and a voice like a muted trumpet; and the wide-ranging New Yorker Nico Muhly comes more squarely out of 20th-century classical composition, writing sweet pieces for strings, woodwinds, voices and other textures.
Prior to returning to Stanford in 2000, he taught courses in rhetoric, composition, writing pedagogy, literature, creative nonfiction, and fiction writing at San Diego State University and the University of Arizona, where he directed the University Composition Board, overseeing assessment, outreach, and writing-across-the-curriculum programs.
Mr. Perkinson called composition "written improvisation".
Then there was a freeform composition written specially for tonight.
Scrambled English of sixth-grade composition written on Norma Shearer, "My Favorite Actress".
"Here's a composition written by my father, Dizzy Gillespie," the saxophonist James Moody deadpanned at Iridium on Thursday night.
Nilas, who has never studied composition, wrote the music on a synthesizer, weaving together the different instruments on different tracks.
