Glamorgan started at 12-0 under cloudy skies but Coad began an early procession, trapping Sam Northeast lbw for 16.
Fisher found late movement to have Asa Tribe and Kiran Carlson caught at slip in successive balls before Coad found the edge of Ben Kellaway’s bat to give Jonny Bairstow the first of three catches behind the stumps.
Ingram and Chris Cooke (20) added 49 against the change bowlers as the clouds lifted, but Fisher returned to have Cooke edging his second ball to the diving Bairstow, and trapped Timm van der Gugten lbw to make it 98-6 at lunch.
South African Ingram, who has made surpassed half-century in each of his 10 championship games this season, led the fight-back in a stand of 63 with Mason Crane (29), who was acrobatically caught by Bairstow hooking at Jordan Thompson.
Dom Bess bowled Ingram in his first over with Glamorgan still 40 short of the follow-on, but James Harris and Andy Gorvin dug in and scrapped their way to the modest target in the afternoon sun.
Coad finished off the resistance by having Harris (40) given leg-before, though he clearly believed he hit the ball, and bowling last man Ben Morris.
Left 27 overs to bat in fine conditions, Lyth and Bean made the most of it as they found the boundary regularly.
Lyth was the more aggressive with eight fours and a six in his half-century before falling to Harris for 55 in the penultimate over.
Yorkshire were left to ponder the timing of a potential declaration on day three, with the possibility of poor weather on the horizon for the final afternoon.
