There are some nice pictures on the web showing the counter-spiralling paths of an electron positron pair produced in a bubble chamber with a uniform magnetic field, for example:-
(source: bigganblog.com)
Would it be practical to produce a cloud chamber and [Helmholtz coils] capable of imaging such events in an ordinary domestic garage? What sort of source would I need? How often might such events be detected?
You need to
Pair creation calls for the highest energy gamma you can get and as much mass in the chamber as you can arrange.
The odds of getting a pair-conversion event are graphed in figure 31.17 of the 2013 Review of Particle Physics chapter on the passage of radiation through matter, but it doesn't hit 10% in air until somewhere between 6 and 10 MeV. While this process can happen as soon as you get energies above $2m_e \approx 1.022 \,\mathrm{MeV}$, you need some energy left over to give the created particles some momentum. The mass attenuation length is graphed in figure 31.16 of the same reference, but for a few MeV gammas you are looking at distances around 20 cm.
To be able to tell that you got a pair conversion event you need long enough tracks to convince yourself that you have a isolated "vee" and to tell that the tracks curve in opposite directions. That calls for a long enough propagation distance for the you to observer that the track is line-like and to see a non-trivial curvature. For arguments sake let's say that a one-tenth radian curve is good enough. That means getting tracks that are at least one-tenth their radius of curvature.
The radius of curvature of a particle in a magnetic field is given by $$ r = \frac{p}{qB} \,.$$ (Note that I don't write $p=mv$ because the pair may be at least moderately relativistic. Just stick to momentum.)
You need to pick a source of gamma rays, and you want it as energetic as possible. For really energetic gammas you need an accelerator based system, but this makes the project many times as big as it started. I'm going to assume you will use a radiological source, despite the low energy and unpredictable timing. Cobalt-60 would be enough if you have patience, but I'd suggest Thorium-232 if you can get it (you'll actually be taking advantage of the high energy gamma from the daughter isotope Thallium-208).
Using radiological sources means that you need a continuous data-acquisition systems of some kind--say digital video.
Finally you have to chose the strength of the magnetic field, and that depends on the expected momentum of your pair, which depends on the energy of your source.
These electron-positron pairs are created by gamma rays. I don't know anything about how to make a cloud chamber, but detecting cosmic gamma rays at the surface of the Earth is very very rare. The atmosphere is very opaque to gamma rays (Source). Cosmic gamma rays burst are commonly detected on satellites orbiting the Earth, but very few make it to the surface.
These images of pair productions are likely from gamma rays created at particle accelerators.
I don't think it would be practical at all: purely technical problems aside, I am not sure you would be able to ensure safety - we are talking about ionizing radiation, remember?
