I stumbled upon this paper recently:
Reforming health care: Evidence from quantile regressions for counts
Journal of Health Economics 25 (2006) 131–145
"Basically, the approach transforms the discrete data problem into a continuous data problem by adding a random uniform variable to each count. The quantile regression functions of the transformed variable can then be estimated using standard quantile regression software. To interpret the results, one can compare the freely estimated quantile functions to those implied by the respective Poisson or negative binomial estimates in order to detect excess sensitivity in specific parts of the distribution, such as the lower or upper tails."
Machado, J.A.F. and Santos Silva, J.M.C. (2005), Quantiles for Counts, Journal of the American Statistical Association, vol. 100, no. 472, pp. 1226-1237.