This program:

// --
interface IfaceWithPrivateFinalMethod {
    private final void privateFinalMethod() {}
}

triggers the error:

X.java:2: error: modifier final not allowed here
    private final void privateFinalMethod() {}
                       ^
1 error

It would seem since private methods are not inherited, they are final anyway and the compiler should allow the combination of private and final to modify an interface method.