@snood,
Yep. We're going through something similar. There is a family of strays living across the street -- a mom and three kittens. We've been calling around (myself and another neighbor) and the no-kill shelters are full and not accepting any more cats, and the only places that will accept cats have told us that the cats (even the kittens) will almost definitely end up euthanized if we take them there.
I've embarked on a campaign to get someone to adopt the kittens but so far no takers. My husband's allergic so taking them in myself is not an option.
One of the places we talked to has traps for rent -- $50, that you get back when you return the trap (so more of a deposit really). If we can't find anyone to take the cats, we'll trap, neuter, release. (The kittens are too small for that now and we don't want to take the mom away yet.)
One piece of advice I got was to use a lacy tablecloth to trap them -- throw it over them and then kind of gather them up (while doing your best to avoid claws and teeth).
Took this picture of the kitties about a week ago:
(They're all healthy btw -- I was crooning at them and making them sleepy, but they are usually bright-eyed and bushy-tailed.)