Pacific Forest Rally (PFR) in Merritt requires a fully prepped car, which actually isn't that bad to get but is still a big jump. There's some ice racing in the winter, possibly rallycross in Hope during the summer as Mark said, and rallycross up at Big White in the early winter that can be done with stock/nearly stock cars. There's also TSD rallies scattered around here, there was a novice event in Mission this past weekend and there's another novice event August 22. The novice events are set at lower speeds on fully paved roads so they're a good way to try out TSD rally with absolutely anything that's road legal. It's also a good way to test the skills and intestinal fortitude of your co driver as they're shorter (about 4 hrs total). They're also cheap, this last one was $40 or $50 with a second route book (which I recommend so the driver can learn the math as well and double check the co drivers work).
Up from that are the full TSD rallies, Thunderbird was in February but No Alibi is June 6/7 in Kennewick, Washington; Heart of Darkness is July 18/19 in Merritt; Totem is Nov 21-22 out of Cache Creek. Most if not all of them offer a free novice school for drivers and co drivers the night before so it's just as feasible to jump straight into one of them.
The sites you want to watch are
RallyBC Home and
Canada West for info on upcoming rallies in this corner of the world.
RBC - WCRA Novice Series is a really good source of info for novices as well.