You could get customers to constantly bank their funds to your exchange's account, and then set up auto-buy order for BTC whenever the payments are sent. If you are using paypal, I think you can do it as well, if you can find an exchange that has paypal. After then, you could set up auto withdrawals with a whitelisted address if they exist on the exchange, or just do manual withdraws weekly.
I don't think any exchange is going to allow you to use funds in your exchange account which were deposited by people other than you. You go through KYC and only you are allowed to deposit fiat in your exchange account.
