stan_lkj_corr.stan

data {
  int N; // number of observations
  array[N] corr_matrix[2] y; // A n-element arrary of observed correlation matrix [N, 2, 2]
}
parameters {
  real<lower=0> eta;
}
model {
  for (i in 1 : N) {
    y[i,  : ,  : ] ~ lkj_corr(eta); // y[i,] and y[i, ,] should also be fine
  }
}