Intervallic approach
The closest method I've seen, and which I've used successfully both for myself and for students, is Keyboard Musician for the Adult Beginner by Frances Clark.
The approach teaches three "landmark" notes (Bass F, Middle C, Treble G), associating the staff position with the piano key such that the note name is unnecessary (except for ease of verbal communication).
After the landmarks are established, the book teaches to read seconds above and below the landmarks. The next chapters introduce thirds, fourths, and fifths, with no mention of letter names.
Other notations — like rhythmic values, rests, and accidentals — and theory constructs — like keys, scales, and chords — are also introduced at logical points along the way.
FACE groups
A second approach, also interval based at its core, but making use of an easily remember mnemonic, is to teach where the FACEs are on the staff and keyboard.
In essence, this is teaching the student to read in thirds and octaves (octaves, since after the E in each FACE is the F of the next FACE).
What's nice about this approach is that there's only one mnemonic, easily remembered, and consistent regardless of clef.