By Bill Cotterell

TALLAHASSEE Fla. (Reuters) - A man convicted of fatally shooting his sleeping wife, then raping and murdering her 10-year-old daughter, was scheduled to die by injection Thursday evening at Florida State Prison after spending almost half his life on death row.

Attorneys for Chadwick Banks, 43, unsuccessfully challenged the state's lethal-injection methods and argued that his post-conviction legal representation was inadequate.

Banks, shot his sleeping wife, Cassandra Banks, at their mobile home near Quincy in north Florida in 1992. He was arrested four days later and confessed that he then killed his stepdaughter, Melody Cooper, after sexually assaulting her.

Evidence and trial testimony indicated Banks was drinking and shooting pool at a neighborhood bar with his wife on the night of the crimes. She went home and Banks followed an hour later.

Banks was sentenced to death in 1994 for the child's slaying and to life in prison for his wife's murder. After some 20 years of appeals in the case, Florida Governor Rick Scott signed Banks' death warrant in September.

It would be the 20th execution of Scott's first term in office, one fewer than former Governor Jeb Bush presided over in two terms as governor, according to the Florida Department of Corrections website. Scott was re-elected this month to his second four-year term.

It would also be the 89th execution in Florida since the death penalty was reinstated in the United States in 1976.

This version of the story corrects first paragraph to show that the 10-year-old was the daughter of Banks' wife)

(Editing by David Adams and Bill Trott)