Not just Invoice payments, you can import and export any data into and out of Zoho Books.
To Import Invoice Payments,
Go to Sales -> Payments Received.
Click on the Import Payments option from the actions drop down.
You will be directed to another page where the data you wish to be imported needs to be uploaded.
Data can be uploaded either as a CSV (Comma Separated Values), TSV (Tab Separated Values) or XLS (eXceL Spreadsheet) file from your hard drive. Also select the character encoding based on your import file and click on Next.
To Export follow similar steps to importing,
Click on the Export Payment option from the actions drop down.
A pop-up will appear with Invoice Payments already selected as the entity.
Pick a format in which it needs to be exported to your hard drive (CSV or XLS).