What word could describe the movement of a parked car inside which a couple is making out?

"Undulate" is a possibility; unlike "sway", it means up and down (OALD, 1).

undulate [intransitive] (formal) to go or move gently up and down like waves
♦ The countryside undulates pleasantly.

(ref. 1 "movement up and down or from side to side") Chryssa's naked body undulated as the whip came down on her skin, leaving hot red welts upon her back, and it seemed to me as if Iullus was watching with more than morbid fascination

(ref. 2 "movement up and down or from side to side") Falling into the rhythm he set, her body undulated with each strong thrust. The tension inside her built again, faster and faster as he increased the tempo. Knowing she was close to climaxing, she encouraged him with hot, erotic words

For a less gentle motion there is "heave".

heave [intransitive] to rise up and down with strong, regular movements
♦ The boat heaved beneath them.

There is also the verb "to bob".

(bob) [intransitive, transitive] to move or make something move quickly up and down, especially in water
♦ an old cigarette packet bobbing along in the current
bob up and down
♦ Tiny boats bobbed up and down in the harbour.

Apparently, despite the dictionary's definition, you can use "up and down" with these verbs. (ngram 1, ngram 2).

• The car undulated up and down.
• The car heaved up and down.

A slightly quirky term for a car rocking up and down is jounce. Oxford English Dictionary, with two vehicle-appropriate examples:

1. intransitive. To move violently up and down, to fall heavily against something; to bump, bounce, jolt; to go along with a heavy jolting pace.

1967 C. O. Skinner Madame Sarah (new ed.) viii. 171 The train..swayed, rocked, jounced and hustled a couple of passengers from their seats.

1971 D. E. Westlake I gave at Office (1972) 55 The two trucks jouncing off along the narrow dirt road through the swamp

Jouncing is rough. Often, jouncing is caused by the motion of the vehicle against rougher roads, as the second half of the definition ("to go along...") and most examples show.

Aggie gave a nod and watched the moped jounce down the country road toward town. (Connie Spittler, The Erotica Book Club for Nice Ladies, 2015)

However, motion within the car can also cause it to jounce:

He moaned again and tried to move. "Jane?" The car jounced with his movement and Jane felt her heart turn over with fear. (Amber Dean, Deadly Contact, 1963)