I am also looking for a solution to this same problem.  I can get the value with

alert(NWF$('#' + javaPlayerName).val())

I cant set the value or get the value for the second item in the list/drop down

alert(NWF$('#' + javaPlayerName).val(2))

What is the version of your form

I am using version nintex forms 2013 version 2.9.0.0

Try this code

var yourControl = NWF$("#"+ jvarCtl);
var value = yourControl.find("option[title='" + CtlValue + "']").attr("value");
yourControl.val(value);
yourControl.parent().find("input").val(value);
NWF.FormFiller.Functions.ProcessOnChange(yourControl);

what is CtlValue ?

The value you want set

Did the solution suggested work for you to set default value to SQL Request control on Nintex Form?