I'm looking for some OS X Lion software that can periodically backup certain folders.
I can't use Time Machine because the storage disk is NTFS and I'm using Paragon to r/w on it.
If you're not looking for any fancy features that NTFS does not have, I'd basically go with Carbon Copy Cloner.
Its features include:
Given a proper NTFS driver, it should work with NTFS drives.
As Lukasa pointed out, adding a
Copied from an Ask Different answer to Enabling Time Machine for a USB HDD with NTFS:
Backup to NTFS
If you wish to use Time Machine in Lion or greater with an NTFS volume – and if you have a write-enabled driver for NTFS:
In some situations you may find that Time Machine simply offers to use an NTFS volume. This may occur if, say, a write-enabled driver for NTFS is installed before a physical disk with NTFS is introduced to OS X.
Restore from NTFS
OS X can read NTFS, and so should be able to restore from a .sparsebundle in this environment.
Whether Recovery OS is similarly prepared to read from NTFS and restore, I don't know.
Time Machine can backup to an NTFS drive using a sparsebundle but there's a bit of work involved. If you've already got a read-write driver like Paragon then your remaining steps are:
The blog post contains a script to do the fiddly bits, especially getting your UUID and creating the preferences file, and to set it as Time Machine backup destination.