Supply of Boiling water without power outlet
Do as others do and use a camping stove. 

They come as gas stoves like this one or even as wood- or charcoal-fired versions (see here). Perhaps an avid camper among your friends could even lend you one, means you'd only have to buy the fuel.

But before you do this check with the local authorities / people responsible for the event whether they are ok with these open-flame stoves at a public event, keep a fire extinguisher ready and ensure noone can accidentally get hurt, especially if lots of people are attending. Ensure the stove is set up properly and on solid ground, not wobbly or uneven. Be careful not to burn yourself or your partner, especially if business gets hectic. You'll also need the corresponding equipment, e.g. a stovetop kettle, a hand-filter or french press for the coffee, and fresh clean water (unless available on-site).