"-ant" or "-ent" words are almost always adjectives. "-ance" or "-ence" are almost always nouns.
"When will it be convenient for you to come over?" uses "convenient" to describe "it", which is the situation or time. "When is a convenient time for you to come over?" means the same thing.
In the same way, "Is this relevant?" uses "relevant" to describe "this".
"Please call me at your convenience." uses "convenience" as a noun, there's nothing to describe. "Convenience" is the state of being convenient. One's convenience is when they find something easier to do.
Convenience can be used as an adjective in one place that I know of: A convenience store is a store that's trying to be convenient. A convenient store just happens to be convenient even if it isn't trying.