We just transitioned to daycare, but the long days that our in home manny was able to afford us were excellent. Also, we didn't have to worry about sick days whatsoever. Manny was perfectly willing to take care of our sick baby in our home.
Try local stay at home mom's with school aged kids, try recent retirees, try people who have recently lost their jobs and want some pocket money until they find something themselves. Ask at your place of worship or community center. You might also try the local pools and ask if there is anyone who tried out to be a lifeguard and didn't make the cut. Those kids have a lot of first aid/ cpr training, and tend to have their wits about them.
As best you are able, try not to start the new job and the new childcare at the same time. You don't want to have to flake out of work to fix a childcare situation which needs some tweaking.
Good luck to you and yours,
F. B.