The only way I know to get totally free disposable baby diapers is by going to a diaper bank. You'll most likely need proof of income and anything else that might be required.
You can get coupons though to save money on disposable baby though. There are coupon websites where you can print free coupons that you can take to the store to purchase baby diapers.
If your'e having trouble paying for diapers for your baby then you might look into switching to cloth diapers instead of disposable diapers.
Cloth diapers cost a little up front but are much cheaper to use in the long run.
You can also reuse the cloth diapers for a second or third baby.
You save money in the long run using cloth diapers and they're much healthier for your baby.