How to set correlational beta prior distribution using jags?

When I'm using jags to do Bayesian modeling, I'm trying to set correlational prior distribution for two parameters that should only take values between 0 and 1. I want to use correlational priors due to theoretical reason, because I expect these two parameters to be correlated in my question setting. I found that without the 0-1 constraint, I can easily use multivariate normal distribution to set correlational priors, such as follows.

mu_prior_mean <- c(0, 0)
mu_prior_sd <- c(5, 5)
mu_prior_corr <- 0.8
mu_prior_cov <- matrix(c(mu_prior_sd[1] ^ 2,
                         mu_prior_corr * mu_prior_sd[1] * mu_prior_sd[2],
                         mu_prior_corr * mu_prior_sd[1] * mu_prior_sd[2],
                         mu_prior_sd[2] ^ 2), nrow = 2)
mu[1:2] ~ dmnorm.vcov(mu_prior_mean[1:2],mu_prior_cov[1:2, 1:2])

However, this won't be able to constrain the parameters mu to be between 0 and 1. What I have tried:

1. The function I(.) does not work on the parameter vector.
2. Use logit transformation

logit(mu[1:2]) ~ dmnorm.vcov(mu_prior_mean[1:2],mu_prior_cov[1:2, 1:2])

But a prior distribution simulation shows that mu1 and mu2 are not correlated, after the logit transformation.

Is there a way that I can set correlational beta priors on my parameter vector mu[1:2]?

Thanks for your time.