I believe there is no option for part payments on the self employed version of QuickBooks (QBSE).

The only solution I was told was to re-issue the invoice as 2 separate invoices. So you would have to credit the existing invoice and raise 2 separate invoices, one for the paid amount and another for the remaining balance... this is because the "invoicing" part of QBSE is not part of the ledger itself and figures do not appear on your tax return. QBSE is for small cash basis sole traders only so if you are requiring "Debtors reports" you will need a business licence from QuickBooks.

I hope this helps guys