Spearman correlations are equivalent to Pearson correlations between the ranks of two variables and Pearson correlations are functions of totals. Therefore, you can estimate Spearman correlations using PROC SURVEYMEANS and a little programming. The method is described in the book "Model Assisted Survey Sampling" by Sardal, Swensson and Wretman. The essential formula that you will need for correlations is found in exercise 13.1.
There are also two Web Examples available at support.sas.com that demonstrate this method. The Web Examples demonstrate how to estimate the variance of a variable and the standard deviation of a variable; correlations are just an extension of the same idea.
http://support.sas.com/rnd/app/examples/stat/SurveyVariance/new_example/index.html
http://support.sas.com/rnd/app/examples/stat/SurveyStdDev/new_example/index.html