Prospects for detection of gravitons?

The short answer is no.

As far as I know the first person to address this issue was Freeman Dyson - at least his is the name you see associated with the question. Googling finds only this article from 2004 that is behind a paywall, though I'm sure I encountered Dyson's ideas some time before 2004.

Anyhow there is a thorough discussion of the problem in Can Gravitons Be Detected? by Tony Rothman, Stephen Boughn. They confirm that the answer is no in practice though they suggest that in principle gravitons could be detected.

The problem is that gravitons interact extraordinarily weakly with matter, and there simply isn't any physically realistic equipment with the sensitivity to detect a single graviton. Incidentally the same problem means it's extremely unlikely we'll ever be able to observe a graviton being produced in a collider.

Well, phenomenologists never give up. Here is a paper peer reviewed which explores the discovery of gravitons in future, but not too far future, colliders.

All one needs is large extra dimensions in a string theoretical model, to give predictions.

Two birds with one stone, graviton and extra dimensions.

Edit with new information:

In the paper, "Using cosmology to establish the quantization of gravity," published in Physical Review D (Feb. 20, 2014), Lawrence Krauss, a cosmologist at Arizona State University, and Frank Wilczek, a Nobel-prize winning physicist with MIT and ASU, have proposed that measuring minute changes in the cosmic background radiation of the universe could be a pathway of detecting the telltale effects of gravitons.

from the abstract :

We argue here, however, that measurement of polarization of the Cosmic Microwave Background due to a long wavelength stochastic background of gravitational waves from Inflation in the Early Universe would firmly establish the quantization of gravity.

The BICEP2 experiment measures polarization, and if the future measurements show gravitational waves the quantized nature of gravity, and therefore gravitons, will have been detected.

My own view differs from the mainstream view. I would say that gravitons have already been detected as I'm in favor of using a rigorous definition of "detection" that is not based on arbitrary rules that we've invented. Any argument about "detection" should be discussed from the laws of physics themselves. I therefore reject the notion that "detection" should always involve some traditional experiment, which in this case should involve some scattering experiment. You can't demonstrate, starting from the laws of physics, that this is the only way to establish the fact that gravitons indeed exist.

The existence of gravitons became a certainty when the existence of gravitational waves became a certainty. And that happened not when LIGO detected the signal from the black hole merger, but much earlier when tests of general relativity were performed back in the 1960s which confirmed its validity in at least the weak field limit.

This proves the existence of gravitons because the moment you have established the validity of General Relativity in the weak field limit, the fact that perturbations in the metric will propagate as gravitational waves is established. Quantum mechanics then implies the existence of gravitons. Now, as Jerry Schirmer points out in the comments, GR may break down before one reaches the regime where we could detect single graviton processes. But gravitons then still exist as quasi-particles at lower energies, and single graviton processes do occur at those lower energies, it's just that we won't be able to see it there due to technical issues.