Convenio translates to "agreement" or "pact." It's a more formal and significant word than a simple "acuerdo" (agreement), suggesting a more serious and established understanding.
In this song, the narrator uses convenio to refer to a clear and established agreement with his partner about the nature of their relationship – specifically, that they would not demand marriage. The use of this word highlights the gravity of their initial understanding and the narrator's surprise when his partner goes against it.
“En Eso No Quedamos” plays out as a firm refusal dressed up in a pet name. The singer opens by reminding a partner of the original terms — “Acuérdate que hicimos un convenio” (“Remember we made an agreement”) — a deal that ruled out demanding anything beyond what was settled. When the partner keeps pushing for marriage anyway — “Me pides que acabemos por casarnos” (“You're asking for us to get married”) — the singer draws the line flatly: “En eso no quedamos, corazón” (“That's not what we agreed on, darling”).
The refusal is an argument for staying free, not a cold one. “Recuerda que fue nuestra decisión, amarnos sin perder jamás la libertad” (“Remember it was our decision, to love each other without ever losing our freedom”) makes the case that the arrangement itself, not marriage, is what keeps the romance alive: “Casarnos para qué, si la pasión aumenta cada vez que nos damos el amor” (“Why get married, if the passion increases every time we make love”).