Adding a custom paint job to an umbrella
That's an imaginative gift!

The silk screen industry has been applying paint to fabric (umbrellas included) for some time. You might be able to by a small amount from a local shop. 

The inks (paints) used are reducible to some degree and may be your answer, as they are both flexible and impervious to water. Your timeline is problematic though, as it does not allow for experimentation and I will not give you a guarantee that one can paint with the medium.