To enter Indonesia I believe a US citizen can just get a 30 day visa on arrival.
As a foreigner, if you stay at a private house, you will need to register with the local police to stay legal. That much should be a free service. Have a photocopy of your passport 'face' and visa page ready for them.
I'm unsure of the answer to the main question but I understand the church service alone has no status in law so no government paperwork would be required. If I'm correct, the local vicar/priest is the only one you need to sort out with.
Atlantis will know far better than I do.