People in the FM district often use the East Area YMCA for before/after childcare. There's one in Manlius and one Fayetteville. The district buses to/from, including for half days.
School-Age Childcare | YMCA of Greater Syracuse
I don't know about care for the 14 month-old. I'd ask the Y people if they have a list of childcare providers for non-school-aged children. There are a few I know, off the top of my head:
SonShine Child Care - Manlius, New York - A ministry of Community Covenant Church
https://plus.google.com/117009115865...39/about?hl=en
Shining Stars, which ck linked already.
https://plus.google.com/108168800492...01/about?hl=en
There aren't a lot of stay-at-home moms who watch children, though there are quite a few SAHMs. Sometimes, there will be postings on Craigslist... I'd probably go through those and set up a meeting/tour of their home and interview. (Definitely use your spidey-sense to filter through the listings. lol) NY limits childcare from the home for up to 2 children, in addition to one's own children, without the mom having to go through training, licensing, etc. It might work out to find a mom in the busing area of the kindergartener's school... to just drop them both off in the morning and pick them up in the evening. And if you don't find any, post what you need and weed through the responses.