Both teams look to snap five-game losing streaks when they meet Thursday in Phoenix in the opener of a home-and-home series.
With 63 points, the Coyotes (29-45-5) are at the bottom of the West standings, three points behind the Kings (26-40-14). Each team will miss the playoffs for a fourth straight season.
Los Angeles finishes its season Saturday against Phoenix at Staples Center, while the Coyotes host Vancouver on Sunday to close out their season.
Phoenix is 3-2-1 against Los Angeles this season and has won two of the last three meetings, including a 3-2 road victory on Jan. 20 in the teams' most recent contest.
The Coyotes lost 5-2 to St. Louis at home on Tuesday. Daniel Carcillo and Jeremy Roenick scored, and Curtis Joseph was pulled for the second time in three games after allowing all five goals in his fourth straight loss.
"The effort was not very good, very average," Coyotes coach Wayne Gretzky said. "You have to play every shift until the very end. It is hard to play now. We understand that. But you have to play hard every night. You get paid until the end of the season and we have to be professional about it."
Roenick, who has just nine goals in 67 games in his 18th season, registered a point in his second straight contest and scored his second goal in 22 games.
Carcillo, who came over from Pittsburgh at the trade deadline, scored his fourth goal in 15 games with the Coyotes, who fell to 2-12-2 in their last 16 games. Phoenix has allowed an average of 4.6 goals during its five-game skid.
"I know there's a lot of incentive just to pack it in," Carcillo said. "But guys like me are playing for jobs next year and other guys want to stick and around and be part of the winning that's going to happen here in the next few years."
Shane Doan, who played in his 800th career game Tuesday, has scored three of his team-leading 26 goals in five meetings with Los Angeles this season. He has gone seven straight games without a goal.
Los Angeles lost 4-2 at Vancouver on Tuesday as the Canucks scored four unanswered goals to erase a 2-0 deficit. Derek Armstrong and Dustin Brown each scored power-play goals, but the Kings were outshot 32-17 and allowed two power-play goals.
Los Angeles' opponents are 7-for-16 with the man advantage in the last three games.
"We were doing good the first period and beginning of the second and after that we took too many penalties and put ourselves in trouble," said Mathieu Garon, who recorded his first shutout of the season in a 4-0 win at Phoenix on Oct. 19. "After that, the momentum changed sides."
Armstrong has four goals and three assists in six games against Phoenix this season. He's registered six points in his last three contests against the Coyotes.