This translates directly to "I have a sister but cousins."
Alternatively, you could use a slightly more nuanced phrase like:
* "J'ai une sœur, mais je suis aussi cousine avec..." ("I have a sister, but I'm also cousins with...") This emphasizes the cousin relationship.
* "J'ai une sœur et des cousins." ("I have a sister and cousins.") This simply states both familial relationships.
The best phrase to use will depend on the specific context and the nuance you want to convey.