In the current jobs climate, its difficult enough to even get through a potential employer's door without presenting can do / can't do. I would say I could work any day, any time. If they like you, they will be more open to negotiation because they will want you.
I did this to get a short term temp job - I now have a permanent pt job with perfect days and times. I wouldn't have got through the door if I had told them how restricted I was!
I would not mention it in the cover letter as you may get weeded out before interview stage for that reason. If you get an interview and they really like you, then they are more likely to be flexible to work around your available days. (Likewise if you get offered the job and decide you really want it, you may be able to find other childcare options for those days.)
I'm assuming that you are applying for p/t jobs in the first place. I personally would not apply for f/t jobs if you are only available p/t, it's wasting their time and may put them off considering you for any p/t jobs that came up in future.
I would put it in writing. When I was looking I'd even apply for full time roles asking if they would consider p/t. I did get an interview or two using this tactic! I eventually did get a p/t role (advertised as p/t).
Personally, I would call and ask before submitting an application as you don't want to waste either your time or their time by applying if its inlikely. You should ask if there is flexibility rather than saying what you can/can't do (unless asked) as it sounds less demanding.