You’d have to convince the IRS that you don’t get any personal benefit from the lessons. Good luck with that. Anyway, charitable contributions have to be in cash or something concrete with cash value (such as stock, used furniture, etc.) You can’t deduct something nontangible, such as improved singing ability. So no.
I can’t give any tax advice, because deductions depend on so many other factors, but I can direct you to the IRS website, which provides documentation describing the VERY STRICT rules regarding “in kind” donations– In particular, the service actually rendered to the nonprofit is what is deductible, not service rendered to a third party.
However, there are many other things that may be tax deductible in your situation–for example, the cost of dry cleaning a uniform, gas to/from the venue, etc., but those are still not “in kind” donations to the church.
If the church recognized Jeannette’s singing as in kind donation, the value of the perticular singing service and cost related to it (such as score and etc) would be tax deductable. However, I think lesson fee is still not be deductable in this situation.