Well, I don't have experience with this but I've been touring day care facilities for our baby and the two I looked at had notebooks/daily report sheets that the caretakers filled out and shared with the parents at the end of each day. So they logged the time of each diaper change (and if it was BM or not), feeding and how much, and nap times and for how long. They also made any other notes that seemed relevant. Then the parents either reviewed the notebook/daily report sheets in the daycare or took them home to review and bring back the next day. Don't know if this could be modified for your situation or not...

I have a nanny and had her do this when she first started. I just created a spreadsheet that had hours down one side and across the top I had pee, poop, feeding, nap. She just put an x in the box when those items happened during the day. Now that my daughter is 5 months, I no longer have her do it since her schedule fluctuates quite frequently and it because somewhat of a pain to keep jotting it down.

I worked at a daycare for over a year and we had daily report logs we did for each child with all the information that you listed above. I now take care of my friends daughter and have taken it upon myself to right down the things on a regular piece of paper. I just write the date at the top and make a note of when she last ate and then any time she eats, sleeps or I change her diaper I write down what time, for how long and what kind of diaper it was. I also make a note of any activities we did, like going for a walk or what books we read. I would just interview and make it clear what you want and if you're nanny/babysitter is the right one for you they will do it. It's up to you to ask them to just write it down or create a sheet for them to fill out through out the day. Good luck.