E.,
Hi. When I downsized to a smaller bag, I used the free formula diaper bag that I received at the hospital. Cheap, yeah, but it hangs off the back of the stroller, no one really sees it. Mine had a small compartment for the change pad, an open outside pocket, space on both ends for bottles, or keys, or cell phone and a decent sized inner space with inner pocket. If you want something to keep stuff cool, buy an insulated lunchbag and use a carbiner clip if you can't fit it under your stroller. (Clip it to diaper bag.)
If that's not an option (and I use this on outdoor park outings, travel and for full day excursions), go for the backpack option. This allows you to be hands free ... of course it does cause a problem with a purse/handbag... you'll have to consolidate only necessities and put them in the pack. I found a wonderful, multi-compartment pack at Target last summer before our plane trip to Canada. (The pack fit diapers, pullups, foldup potty seat, wipes, snacks for both kids and me, sippy cups, bottles, purse stuff, etc... etc...) Since I was traveling alone with the kids, it was a lifesaver!
You could also buy a bag clip and/or other accessories to add to your stroller to optimize space.
Good luck!
T.
Mommy to Katelyn, 3.5 and fully potty trained (no diaper bag for her!
AND Matthew 18 months... the diaper bag is all about him now!