I also think they are fine just to ask. They took on a puppy and with that comes responsibility. Sounds to me like they are taking it seriously.
For the poster who said someone could pop round and let it out to wee - that's what you do with an older dog who is used to being left and can hold on. An untrained puppy won't know it needs to wait until it's let into the garden. Dogs become flexible and adaptable as they get bigger, but you have a settling in period first. Like kids really - you have a bit where you give yourself time to let things settle down and then it gets easier and you can start getting on with stuff again.
It's not human, no, but it is an animal with the ability to feel fear and distress and if you choose to take it on, then you have a responsibility towards it. If you don't take this stuff seriously, then you end up with problem dogs who don't behave, won't settle, get anxious and chew things, bark and howl when they are left, and everyone says "Well why didn't you look after it properly - taking a dog on is a big responsibility you know."
They are clearly planning ahead, and knowing that the christening is being planned too and that there might be a problem, they've started to try and think about a way round it. There might not be anyone who can come and puppy sit - same way as some people don't have anyone to babysit. This time next year it probably wouldn't have been a problem - it is the fact the puppy is so young. Leaving it in the car will probably result in a car covered in crap and vomit.
For what it's worth, I planned the time of year I got my puppy, so I had the time to get her settled in and sorted, gave myself a few months of letting her adjust (quick trips out without her to start with, followed by slightly longer trips etc) and now she is the most laid back, chilled out hound ever, who is dead easy to be around, and easy to leave if I need to attend things. It won't stop them doing stuff forever - they just have a critical period to get through first.
So they've asked. You can say no, or work with them to come up with another idea. If the date is important to you then you might have to live with them not being there but it sounds as though they are important to you, so talk to them and see if they've come up with any other ideas. (If you've had time to go away and think about it then chances are so have they - they've responded the way I probably would to begin with, but then after coming off the phone my mind would start going over it - what are the ways round this? They might have more ideas now they've had some time to mull things over.)