News Corp.'s Twentieth Century Fox is trying to slow the arrival of its DVDs in low-cost rental kiosks run by Redbox, the studio said Wednesday.

Redbox, a unit of Coinstar Inc., rents DVDs for just $1 a night, which some studios believe is contributing to the slumping DVD sales market. Studio revenue from disc sales to retailers and rental outlets is due to fall by about $850 million to $12.9 billion this year, according to Adams Media Research.

Fox...