You could get Documents To Go Premium (allows for direct connection to a DropBox account or other Cloud services) and create a Spreadsheet. DocsToGo is nearly a "must have" anyway. Using DropBox you can install it (free) on your desktop and it will sync up between iPad and desktop. Would be a simple spreadsheet, really.
Across the top could be Date Mowed and the rows could be the client name/address. Yes/no under the date could indicate whether they paid or not.
Is there a specific app for something like this, possibly.