My scala/sbt project uses grizzled-slf4j and logback. A third-party dependency uses Apache Commons Logging.
With Java/Maven, I would use jcl-over-slf4j and logback-c
Heiko's approach will probably work, but will lead to none of the dependencies of the 3rd party lib to be downloaded. If you only want to exclude a specific one use exclude.
libraryDependencies += "foo" % "bar" % "0.7.0" exclude("org.baz", "bam")
or
... excludeAll( ExclusionRule(organization = "org.baz") ) // does not work with generated poms!