It depends on what you count as "a small amount".

Because polonium is an unstable radioactive element with a really short half-life for even the most stable isotope, the only practical way to make polonium would be a particle accelerator or a nuclear reactor (a Farnsworth Fusor would of course be both).

Trace levels: chemical extraction from uranium ore

I say "practical" because it was first extracted from uranium ore in 1989, but in tiny quantities. If only trace levels are sufficient for your story, that's certainly the easiest way — following the lab books of Marie and Pierre Curie and of Willy Marckwald would be, perhaps not "easy" but certainly much easier than building an appropriate nuclear reactor or particle accelerator.

Low levels: DIY particle accelerator

The Wikipedia page you linked to says ²⁰⁸Po "can be made through the alpha, proton, or deuteron bombardment of lead or bismuth in a cyclotron", and although I don't have the book that Wikipedia cites as a source for this to say how powerful an accelerator you'd need for that, cyclotrons are fairly straightforward to build, having been superseded in the 1950s.

The problem is (as with the Farnsworth Fusor) that the most likely thing that happens when you smash two atoms together is they just bounce off. I don't know the exact probabilities of nuclear-reaction vs bouncing, and this is something that I wouldn't be surprised to find is genuinely classified as a state secret by every nation that has so much as a nuclear reactor program, but if it isn't classified then the key phrase to search for will be the "nuclear cross section".

Just enough to be a problem: DIY reactor in your mother's garden shed

Based on what happened in the incident of the Radioactive Boy Scout, and compared to the fact that I've never ever heard of anyone disposing of a home-made Farnsworth Fusor by declaring it a Superfund hazardous materials cleanup site, I suspect that DIY chain reactions are much more capable of producing "interesting" things like polonium than are mere accelerators-based setups. Indeed, the existence of natural nuclear fission reactors shows that no special isotope purification is needed, isotope purification being both really difficult and important for many nuclear reactor designs.

Isotope purification of heavy elements is so difficult that it's unreasonable for any private individual or organisation to do it at a scale that would make a reactor viable — it is a necessary step for nuclear weapon production, and the difficulty of isotope purification is why so few nations have a nuclear weapons program. Instead, consider the pressurized heavy-water reactor, as that uses natural (unenriched) uranium. PHWR requires D₂O, but that is much easier to get (or manufacture) than enriched uranium as hydrogen⟷deuterium is a much larger relative mass difference (100%) than ²³⁵U⟷²³⁸U (1.3%).

It depends on what you count as "a small amount".

Because polonium is an unstable radioactive element with a really short half-life for even the most stable isotope, the only practical way to make polonium would be a particle accelerator or a nuclear reactor (a Farnsworth Fusor would of course be both).

Trace levels: chemical extraction from uranium ore

I say "practical" because it was first extracted from uranium ore in 1898, but in tiny quantities. If only trace levels are sufficient for your story, that's certainly the easiest way — following the lab books of Marie and Pierre Curie and of Willy Marckwald would be, perhaps not "easy" but certainly much easier than building an appropriate nuclear reactor or particle accelerator.

Low levels: DIY particle accelerator

The Wikipedia page you linked to says ²⁰⁸Po "can be made through the alpha, proton, or deuteron bombardment of lead or bismuth in a cyclotron", and although I don't have the book that Wikipedia cites as a source for this to say how powerful an accelerator you'd need for that, cyclotrons are fairly straightforward to build, having been superseded in the 1950s.

The problem is (as with the Farnsworth Fusor) that the most likely thing that happens when you smash two atoms together is they just bounce off. I don't know the exact probabilities of nuclear-reaction vs bouncing, and this is something that I wouldn't be surprised to find is genuinely classified as a state secret by every nation that has so much as a nuclear reactor program, but if it isn't classified then the key phrase to search for will be the "nuclear cross section".

Just enough to be a problem: DIY reactor in your mother's garden shed

Based on what happened in the incident of the Radioactive Boy Scout, and compared to the fact that I've never ever heard of anyone disposing of a home-made Farnsworth Fusor by declaring it a Superfund hazardous materials cleanup site, I suspect that DIY chain reactions are much more capable of producing "interesting" things like polonium than are mere accelerators-based setups. Indeed, the existence of natural nuclear fission reactors shows that no special isotope purification is needed, isotope purification being both really difficult and important for many nuclear reactor designs.

Isotope purification of heavy elements is so difficult that it's unreasonable for any private individual or organisation to do it at a scale that would make a reactor viable — it is a necessary step for nuclear weapon production, and the difficulty of isotope purification is why so few nations have a nuclear weapons program. Instead, consider the pressurized heavy-water reactor, as that uses natural (unenriched) uranium. PHWR requires D₂O, but that is much easier to get (or manufacture) than enriched uranium as hydrogen⟷deuterium is a much larger relative mass difference (100%) than ²³⁵U⟷²³⁸U (1.3%).