Coles, one of the smallest players on the men's Professional Golf Association tour, shot a big 3-under, 69 Friday and climbed to the top of the leaderboard with Quigley, who shot his second straight 67. They are tied at 10-under-par, 134 midway through the event.
World number two Singh tied the course record with an opening round 8-under par, 64, but was not able to maintain the lead or momentum, and settled for a 1-under, 71 Friday.
Daly, who has finished in the top 10 at the Houston Open each of the last two years, has not won a major golf tournament since the Buick Invitational in February, 2004.
Joining Daly and Singh one shot off the lead are Americans Joe Ogilvie and Jeff Maggert.
Some information for this report provided by AP and Reuters.