Not really sure why you would ever need to try to "annualize" covariance with respect to rates of returns.
Any reason you'd have to do this?
Statistically COV(cX,kY) = ck*COV(X,Y)... in your case, if X and Y are monthly and you "annualize" them, you'd have to multiply your covariance by 144.
Similarly VAR(cX) = c^2*VAR(X)
One other thing about annualizing COV that didn't enter my brain last night... as you add more points to the data set, you are just making it more accurate. So, you really wouldn't need to "annualize" it.
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