Looking at the list (http://edwardlib.org/api/reference), the only distribution over positive definite matrices is the Wishart. An alternative is to appropriately transform/constrain a distribution over matrices, or build your own.
If you're okay with point estimates, you can perform point estimation without any prior over the covariance (e.g., maximum likelihood). Simply parameterize the covariance matrix as a constrained
tf.Variable. This is a common application with linear mixed models.