What would be the advantages and drawbacks of a single-propeller tiltrotor? When looking at existing tiltrotors, most of the designs use two propellers, sometimes four. helicopters (and light planes), on the other hand, generally use only one propeller.

Have there ever been designs or proposals using a single rotor (or contra-rotative rotors on the same axis) instead? If so, what advantages and drawbacks did they have? If not, are there specific reasons why this configuration is always ignored?

The most obvious one would be that the engine would sit right on the cockpit, taking its place or at least blocking visibility. But we can imagine a tiltrotor UAV where this would not be an issue.

For the needs of this question, tail-sitters like the Convair XFY Pogo are not considered tiltrotors, as the entire craft changed orientation instead of only the engines.
Such an aircraft can't exist.

Helicopters don't work with a single rotor, they need at least two of them to counter torque. There are several popular designs, including conventional, coaxial, intermeshing and tandem rotors.

All tiltrotors operate as tandems in helicopter mode. It's the only setup where both rotors can be placed at the nose, tail or wings. In all other designs, at least one of the rotors needs to be mounted in the middle, above the center of gravity, where it can't be tilted without crashing it into something.