generate Binomial (not Binary) data

  "Let i indexes  a subject and Y_i = (Y_i1, Y_i2,...,Y_iT)
   be a vector of binomial variables for subject i  such that
   Y_it ~ Bin(n,p_t) with t = 1,2, ....T.
   A simple correlation I would like to have is :
   corr(Y_ij, Y_ik) = c for all (j,k)"

I have only seen only a portion of this discussion, so I hope that
the following is not unrelated to the question.

Would it be Ok to generate a sequence p_1,...,p_t, ...p_T
from a Beta stationary process (which exists, actual more
than one sort), and then sample from Bin(n,p_t)?

Alternatively, some 20 years ago, there was a stream of literature 
for discrete sttionary processes, based on the idea of "thinning"
a discrete variable. There are for sure stationary processes
with Negative binomial distribution of this sort. I have
not followed that literature, but it is conceivable that
the similar process for the binomial case has been considered.

Best wishes,

Adelchi Azzalini

Adelchi Azzalini  <azzalini a stat.unipd.it>
Dipart.Scienze Statistiche, Universit? di Padova, Italia
tel. +39 049 8274147,  http://azzalini.stat.unipd.it/