If I purchased an original oil painting - I know that this piece belongs to me.

If I was to make prints of this painting - for sales purposes... would I be within my rights, as the owner of this piece to do so, or would I need permission and/or pay royalties to the artist - for each print that was sold?

To the best of my knowledge, Tree, you bought the painting, not any re-publication rights. However, your planet's law may be different than US law.

The actual producer of a work owns the copyright, not the current owner.

'Currently, a copyright lasts for the life of the author plus 70 years. If the work is one that is created for someone else (a "work for hire") or if it is anonymous or pseudonymous (i.e., pen name), it lasts for 95 years from the year of first publication or 120 years from the date of creation, whichever expires first. Publication includes loaning, leasing, selling, or giving away copies of the work.
Have a read at this, it will probably make more sense.Here

All of which explains why big auction houses, such as Christie's,state in terms when a particular work is sold with its reproduction rights. This sometimes happens with photographs at auction, when the vendor is some agency or newspaper that took the rights under contract with the photographer employed, but is rare indeed for other works.

There can be fun and games with copyright. Here in France a photograph, by Robert Doisneau, showing a couple kissing outside a Parisian town hall gave rise to some. It became famous. Numerous couples came forward to claim their rights under copyright,claiming to be the couple in the picture. It had been taken many years before and it seems that the claimants were spurred by the death of the photographer. This was all a surprise to most outsiders because the photo was always touted as being a candid shot of ordinary passers- by; Doisneau had not publicized the fact that he had hired a couple of student actors for it, in an assignment to show post-war Parisian life

Thank you very much to all of you. This pool is forever filled with knowledge to sip from.