Unmanned　aerial　vehicles　(UAVs)　are　widely　adopted　as　aerial　relays　assisting　seamless　coverage　due　to　flexible　deployment　and　high　maneuverability,　but　their　service　time　is　considered　as　the　bottleneck　due　to　the　constrained　energy.　The　energy-efficient　intelligent　reflecting　surface　(IRS)　is　adopted　in　the　UAV　system　for　long-term　service.　In　this　paper,　the　cooperative　relay-transmission　in　UAV-IRS　based　terahertz　(THz)　networks　is　studied,　where　UAVs　with　IRSs　as　relays　facilitate　long-term　seamless　coverage　through　THz　transmission,　and　the　maximum　transmission　capacity　based　on　sum　rate　and　energy　consumption　is　formulated　as　a　maximization　problem　to　optimize　UAV　altitude,　relay　selection　and　user　association.　In　the　single-user-single-UAV　scenario,　how　relay　selection　is　affected　by　the　IRS　element　number　and　UAV　transmitting　power　is　analyzed.　In　the　multiple-user-multiple-UAV　scenario,　the　maximization　problem　is　decomposed　into　three　sub-problems　and　solved　by　an　alternating　optimization　method:　optimizing　UAV　height　using　gradient　descent　and　interior　point　algorithms,　solving　relay　selection　as　a　linear　programming　problem　by　continuous　variable　relaxation,　and　optimizing　user　association　as　a　knapsack　problem　through　association　matrix　transformation.　Simulation　results　demonstrate　the　effectiveness　of　the　proposed　method　and　indicate　that　the　cooperative　relay-transmission　scheme　achieves　quasi-optimal　performance　when　compared　with　existing　schemes.