K.B.
Unfotunately, I work late and generally wake up later otherwise I would be willing to do it myself.
I have found that students tend to be a nice source but unfortunately are not generally available suring business hours. There are some "sick care" daycare services out there where the sitter goes directly to the home- but I believe they tend to be costly. (still worth looking into though). I think you best bet would be to post something in a church where there might be some elderly retired women that might be able to do it at a reasonable price (and have the Time!)
The hard part with sick kids is that they are so miserable so you really want to leave them in their own environment if possible.
Sorry I couldn't be of much help. I think the difficulty is they need to be available last minute and so early.