Is there a way to create a recurring purchase invoice and / or order similarly to the recurring sales invoices?
Only by creating a clone of a previous purchase invoice
Indeed that’s what I’ve been doing. But I was hoping for something that
works more ‘effectively’ so that I don’t have to keep remembering 
Not necessarily more effective, but you could clone a multiple of times in the one sitting.
If the cloned invoice is for rent, on Jan 1, you could clone 12 times for the year ahead and then Manager will pick up each clone as the dates pass - saving the remembering.
Or if the Invoice & payment occur within the same month and you use Import Bank Statement, then Bank Rules could be a solution.