The phrase "were contingent on" is often used to express that something was dependent on another factor or condition. Synonyms for this phrase could include "hinged on," "relied upon," "rested on," "depended on," "hung on," or "was subject to." These synonyms can help to convey the same meaning in different ways, allowing for more variety in language and writing. For example, one could say that the success of the project hinged on the approval of the board of directors, or that the outcome of the election was subject to the voters' decisions. Using different synonyms can help to add nuance and sophistication to language, making it more engaging and interesting to read.