Parsimonious modeling of the within-subject covariance structure while heeding to its positive-definiteness is of great importance in the analysis of longitudinal data. Using the Cholesky decomposition and the ensuing unconstrained and statistically meaningful reparameterization, we provide a convenient and intuitive framework for developing partially conjugate prior distributions for covariance matrices and show their connections with the (generalized) inverse Wishart priors. Our priors offer many advantages in regard to elicitation, positive definiteness, computations using Gibbs sampling, shrinking covariances toward a particular structure with considerable flexibility, and modeling covariances using covariates. Bayesian estimation methods are developed and the results are compared using two simulation studies. These simulations suggest simpler and more suitable priors for the covariance structure of longitudinal data.