Thanks for you question! Directly in Canyonville, there are several parks that are dog-friendly. Charles V Stanton Park is right off I-5 (hard to miss), and fairly large, but does get some freeway noise. If you take Tiller Trail Highway, however, you arrive at two smaller parks, Herberts Pond Park and Canyonville County Park (this one is right on the Umpqua, which is nice for dogs who like to swim). South of Canyonville, you can also find Canyon Creek Forest State Park, the largest by far. There are some walking trails in that park that would be a good bet.
We hike quite a bit out the Waterfall Highway (138), which you can connect to north of Canyonville at Roseburg, but most of these trails are short, leading to waterfalls, and may not be ideal for dogs.
Hope this helps! Enjoy the area!