I'm tired, so I'd like to ride the coffee cup ride and relax.

Literal

Tired [because-から], coffee-cup [onto-に] ride [then-て] slowly want-to [copula-です].

コーヒーカップに乗って refers to the amusement park 'tea cup' ride — a whimsical choice for relaxation. ~たいです politely expresses the speaker's desire. An unexpectedly playful sentence.