Car horn only works during morning period

Weather can make old circuits behave in a ghastly way. I myself experimented a faulty A/C clutch coil during a cold spell (it showed the signs of a false contact since it intermittently lost continuity at the terminals), that apparently fixed itself when warmer and more humid weather came back (in the meanwhile, i've bought a spare coil just in case it fails definitely). The "i need to apply force" part, provided you're referring to the switch in the steering wheel, likely means that the problem isn't in the relay, but in the switch you're actually pressing. Try disassembling it and checking for any oxidation or false contact.

If you need to press the horn harder when the vehicle has been warmed by the sun then the issue must relate to the plastic trim around the horn push expanding and becoming resistant to pushing.

My first guess at the way to fix it would be to remove the plastic trim covering the horn push and applying white silicone spray grease to the rear face of the plastic in the parts it clips into and if applicable, moves down (sometimes you find tubes or slots behind horn pushes intended to guide the plastic along).