No day book / bank book in SAP. Any work around to list all the payments made (with out going through each of the GLs) for a given day / period ?

You can write a query or get the tables through SE16

If you have used a unique document type for your outgoing or incoming payments, you may use that document type as a filter when you inquire your payment transactions in either the GL's Line Item Inquiry (tcode: FBL3N) or Vendor Line Inquiry (tcode: FBL1N) or Customer Line Inquiry (tcode: FBL5N).