target has luvs for $7.99 there is a $2 off coupon on the generator (exp. 8/31) plus luvs just sent out $2-$2.50 off coupons to certain markets in the mail so if you can trade for those...pretty cheap diapers
A Full Cup - Coupon Generator
you can also use tru/bru coupons with mfg and tru clearanced out the old packaging of their especially for baby brand...you may find some old packages here and there. Also, tru and bru frequently have diapers in their bathrooms at the changing stations so it's a great way to try their brand out without having to spend the money!
Meijer lowered their store brand diapers to $6.99 a jumbo pack.
cvs frequently (at least once a month) has their store brand diapers on sale buy one get one free or b1g1 50% off($7.99) my neighbor swore by these when she had her son...she said only buy the supreme type the CVS Cradlers and Cruisers are comparable to Huggies Supreme diapers. Remember you can use a $2 off $10 any CVS brand AND a $4 off $20 ANY store purchase (there is a $10 off $50 any cvs brand purchase out right now if you are gung-ho)...that's an additional $6 off of a $20 purchase when you wait for the sale. I bought these for my new baby and got 10 packs for $20 (during bogo sale with LOTS of coupons, ecb, and overages) when I found out I was pregnant so I haven't ripped them open yet because we JUST got out of the newborn size and I still had some swaddlers from the hospital as well as a pack of huggies from my friends stash that was barely used.
Wal-mart is known for the white cloud brand of diapers...some people SWEAR by these and they are only $6.97 a jumbo pack.
My babysitters church has a "giving closet" for young/struggling moms that need a hand up.
Another option is going to a parenting class. Apparently people bring tons of coupons and formula checks with them because (at least in our area) most of them are on wic and don't do coupons or need the formula checks. These are usually for new moms (single) but I don't think they discriminate. This would be a way to get the coupons at least. Check with your hospitals and peds office as a resource.
Make your own and do the cloth thing:
Sew Your Own Diapers Cloth Diaper Resources, WAHM Directory, Reviews and Information
And...in the words of my mother in law...who cares what the brand is...it's for poop (well, she said another "choice" word but it would be edited here

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hope this helps!!