It's important to get the two coins on the second turn of Sweet Sweet Canyon's first lap. This is the best start you can make, so if you miss them, hit restart and try again.
When jumping over the blue hill after the water, try and be on the right hand side to make the drift that follows easier to make. This also gives you a much greater chance of grabbing more than two coins on the turn.
Boosting through the doughnut at the end of the lap is the trickiest part. Get as close to the chocolate before using the boost, staying away from the Petey Piranha to the left. As soon as you use the mushroom, start drifting, as you'll naturally run wide and need to turn as much as possible to avoid hitting the wall. Hit the jump and boost across the start finish line into the next lap.
Mario Kart 8 gameplay video walkthrough: Sweet Sweet Canyon fastest time guide