In QED, the electromagnetic field is quantized in wavepackets that we affectionately call "photons." We picture them as particles. Yet we all know that macroscopic electromagnetic fields (such as those that zap us when walking across a carpet or the refrigerator magnet) are described by classical fields that make no mention whatsoever about photons. Is this a contradiction?
No. The way we "glue" these two descriptions together is as follows: the physical (quantum) state that corresponds to the classical electromagnetic field is a COHERENT STATE of photons - these states are not eigenstates of the number operator, but are a special linear combination of wavefunctions of 1, 2, 3, ... photons! Remember, this is quantum mechanics and we can do this.
Those who have studied QM should know that when you have a simple harmonic oscillator, the coherent states form the "semiclassical" states; that is, states whose quantum numbers describe (average) position and momentum. So these states behave as classical states.
If you take QED, and study NOT the states of definite photon number, but these coherent states, you will find that CLASSICAL E&M emerges!
Now to the extent that the graviton approximation makes sense (low energy, low curvature, etc): this argument follows word-for-word in the case of GR! Instead of using the "graviton-number states" we use the "graviton-coherent-states", and we find that these states correspond to CLASSICAL gravitational fields described by the classical Einstein equation.
So there is no contradiction between the "graviton" description and the "manifold" description of gravity, just like there is no contradiction between the "photon" and "field" description of E&M.
Of course, gravity is much more complicated than E&M, since it's a nonlinear theory, etc. But to the extent that the "graviton approximation" makes sense, this is not a real concern. It just means that the "coherent states of quantum gravity" are more complicated than the corresponding QED states.
Hope that helps!