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bayesian conjugate priors for the double exponential distribution?

Johannes Björk 
Dear all,

I'm trying to fit a GML model (a ANCOVA using rjags) where the predicted/dependent variable y is a index ranging from 0-to-1 (hence continuous) and is negatively skewed (see histogram below).

While googling, I came across the Gumbel Min distribution- aka log-Weibull / double exponential / Laplace distribution. 

The double exponential is pre-defined in JAGS. Hence I could try out something like
y[i] ~ ddexp (mu[i], tau) 
where
mu[i] <- a + b[ecotype[i]] * (lat[i]-mean(lat)) + b[ecotype[i]] * (lon[i]-mean(lon))

...But is there any bayesian conjugate priors for the double exponential likelihood distribution? 

And would it be correct to use the double exponential distribution in this case?

Any pointer would be very much appreciated, thanks!

Cheers,
Johannes