I have a couple of my customers that send me $$ viaC2it. C2it is by CitiBank, and is FDIC insured. As well as it doesn't cost anything to sent/receive money. Unless you're sending money to someone that's international - then it costs $10.
They don't have a payment accepting think like PayPal, (cart/links, etc).
But maybe with some coaxing, they can integrate something into their system.