Answer:
saldrían
The conditional tense is used when talking about hypothetical situations and possibilities. Moreover, you can make polite requests using this tense. The verb that we need to conjugate in the conditional tense is salir. The sentence ellos no ________(salir) a cenar stands for the third person plural because of the subject pronoun ellos that means they, so the conjugation of salir for the third person plural in the conditional tense is saldrían. You must take away the ir ending of salir and add drían to the end of sal resulting in saldrían. Finally, we can write this sentence as follows:
Melo y Antonia siempre salen para la cena. Ellos se quejan de que gastan mucho dinero pero no les gusta cocinar. Yo sugiero que ellos cocinen en vez de salir. Antonia dice que si tuviera un chef, ellos no saldrían a cenar.