Hi @hillel, welcome to the forum.
@txnelson gave you by far the most powerful approach.
Perhaps a more simple approach can be the following:
produce the correlations using the multivariate platform. There, ask for the pairwise correlations. Right click on the pairwise correlation table and select >> Sort table >> By Pvalues >> ascending.
 
using a script its should look like this:
 
dt = Open( "$SAMPLE_DATA\semiconductor capability.jmp" );
Multivariate(
	Y( :NPN1, :PNP1, :PNP2, :NPN2, :PNP3, :IVP1, :PNP4 ),
	Estimation Method( "Row-wise" ),
	Scatterplot Matrix( 1 ),
	Pairwise Correlations( 1 ),
	SendToReport(
		Dispatch( {}, "Correlations", OutlineBox, {Close( 1 )} ),
		Dispatch(
			{"Pairwise Correlations"},
			"",
			TableBox,
			{Sort By Column( 7, 1 )}
		)
	)
);
You can also make a data table from the pairwise correlations and take things further.
 
Let us know if it helps,
Ron