I just came across this in the Shakers' first song collection, Millennial Praises (1813):

                   There are Eunuchs

                IN ancient days, the scripture says,
                That lust was so despised,
                To get a name of better fame,
                Some chose to sacrifice it:
                For their distaste to things unchaste,
                Great princes sought their favour,
                To guard the place from actions base,
                And all unclean behaviour.

                2
                Bed chambers were their constant care,
                Hence they obtain'd their title,
                Which simply means, female guardians,
                Who every passion bridle.
                Such foes to lust, when put to trust,
                Were faithful in their station,
                And by their fruit gain'd such repute,
                They almost ruled the nation.

                3
                From eunuchs then, tho' made of men,
                Much light and truth descended,
                Since by that line, God did foresign
                The work which he intended.
                By all the wise, who virtue prize,
                The name was still revered,
                Till in that name the substance came,
                And Christ himself appeared.

                4
                Hence from his throne he then made known
                The way of self-denial,
                And eunuchs were call'd forth to bear
                The gospel's fiery trial:
                Lust-hating men were chosen then,
                Unto a work still greater,
                And their employ was to destroy
                The beastly law of nature.

                5
                He comes again, on earth to reign,
                His court is now erected,
                A mansion sure, for virgins pure,
                Where they can be protected;
                While eunuchs clean, are their guardians,
                His glory in the center,
                No lustful man, then ever can
                His sacred chambers enter.

                6
                Tho' men of wit, search sacred writ,
                And read the lifeless letter,
                And rack their sense with vain comments,
                It never makes them better.
                The case is plain, who now shall reign,
                The elder or the younger?
                And who shall be the sapless tree,
                The eunuch or fleshmonger?

                7
                Ye, who were led from nature's bed,
                Like bullocks to the slaughter,
                You have a name of better fame,
                Than that of son or daughter;
                Your root, we know, will spread and grow,
                Sap'd with the Holy Spirit,
                And none but these green olive trees,
                Christ's Kingdom shall inherit.

No tune mentioned, though. ("Mr Tambourine Man" sorta fits).

And according to this srticle on the Castrators of Russia, they had quite a lot of their own religious songs:

http://etor.h1.ru/castrati.html

though there is no mention of any being written down or recorded.

Is there anything singable out there?