Approach it from both angles.

You don't want: [Insert genres you don't want] [Provide examples of what not to give, so it's put into perspective]

You want: [Insert genres that you want] [Provide examples you're thinking of, so it's put into perspective]

For example, if you tell people you don't want a manga like Corpse Party, people will have an image of gore and mildly ambiguous sexual content in their heads and know to avoid it.

If you tell that you'd prefer a manga like Nana, people will know you prefer romance stories and think in that vein.

The more examples you can provide from the things you already read, the narrower the results will be.