Please note that the approach described in the paper suggested by @Marsu_ is a Bayesian rather than a frequentist one. This means that the intervals it provides, despite what the article claims, are credible intervals, not the confidence ones; and those are in fact very different in interpretation.
The Bayesian approach is assuming that the parameter of interest is a random variable having a prior distribution, and the credible interval bounds are fixed as encompassing a given probability mass of the posterior distribution of that parameter. The prior is chosen through some considerations external to the inference problem; the article itself suggests several alternatives.
From the frequentist standpoint, the parameter is constant and the interval bounds are random variables; the confidence level represents how often on average the true value of the parameter will fall into the resulting confidence interval if the sample was re-drawn multiple times from the distribution.
See Credible interval and Confidence interval: Meaning and interpretation for more information.
So it seems the only remaining options for proper confidence intervals are resampling-based methods like bootstrap or jackknife proposed by others.