An element that is radioactive will always be radioactive until it has decayed into a 'stable' element. So you can't take plutonium and make it non-radioactive. If we could, it would solve a lot of problems in this world. For the man-made elements, scientists have theorized that there may be an area of greater nuclear stability as the atomic number increases, but greater nuclear stability just means a half-life of a few days maybe and not the fractions of a second that the newly made elements exist for. It's just that once the atomic number of an atom gets above 83, there's not enough room in the nucleus for all those particles. It's just energetically not favorable for the atom to remain as it is. Hence it becomes radioactive. (Even for two elements with atomic numbers below 83 the combination of protons and neutrons in the nucleus just cannot remain stable. This is why Technetium and Promethium are radioactive. They just don't have a way to maintain a stable nucleus). So as of right now, unless there is some massive breakthrough (and I mean MASSIVE) in the world of nuclear physics, creating a non-radioactive man-made element is just not possible.
As for taking a non-radioactive element and making it radioactive, that is easily done. If a stable isotope of an element absorbs the particles given off by a radioactive isotope, it may form a radioisotope either of it's own or another element. (I.E. if it were to absorb a neutron it would remain as it is but may turn out radioactive. If it absorbs an alpha particle it would no longer be the same element, but it might be radioactive). I think a good example of this is Beryllium. If non-radioactive Beryllium metal absorbs an alpha particle, it will radioactively decay and give off a neutron. (Be-9 + He-4 --> n + C-12). So the Beryllium does become radioactive and then decays via neutron emission and forms carbon-12. (That's the one example I can think of at the moment, but I'm sure there are a few better ones)