Two glues I've had excellent results with:
Amazing Goop, available at Lowe's, Home Depot, etc. I repair saddles, rack trunks, and even shoes with this stuff. Excess wipes off easily in the first few minutes, sets strong enough to hold heels onto dress shoes, so it'll hold your saddle cover.
Automotive Upholstery Cement, (various brands) available at Pep Boys, Auto Zone, etc. This is the stuff they use to hang headliners and door panels. It's extremely pungent, but holds very well. I had some left over from a car project... Fixed a Trek saddle with it... Like yours, the cover was coming off from underneath. It's still working, fourteen years later...