We have our Baby Do Good program where we donate a lot of cloth diapers to charities and it becomes their onus to give these diapers to whoever they see fit.
Earlier we would give out cloth diapers to deserving families like yours but there was never any acknowledgment once the diapers were received. Again we need feedback from families not so that we feel good about ourselves, we need it because we have to be accountable to our paying customers for the diapers that we are giving out.
We donate regularly to Giving Diapers, Giving Hope (US based), Cloth For a Cause (Canada) and the Rebecca Foundation.
Get in touch with these fine organizations and they will be more than happy to help you.