Fake nails is about the only thing I can think of. I'm sure other classical guitarists come across the same problem so do a Google search and see if there's anything specific made to do the job.
They don't have to be very long, just long enough to extend past your fingertip. Sand them down to shape with some fine sandpaper.
The only other alternative I can think of is fingerpicks..although I tried them once and they were too awkward.