I always use the Motocross Bike on the moon stage.
When fully upgraded the Motocross Bike spins very quickly (courtesy of the Mid-Air Control upgrade), and when combined with the low gravity of the moon you can get up to 20,000 coins each time you leave the ground.
The moon stage is also described as good for farming (coins) on the wiki :
Its main characteristic is low gravity.
It is also very useful for farming as air times are usually 10000
+.
Image from the wiki
gaming.stackexchange.com/users/77290/Caleb
I haven't played in quite a while, but I always found the race car on the highway stage to be a pretty fast way to gather a lot of coins.
Quickly reaching the high-value coins seemed to be a pretty efficient way of coin farming.
You may also want to look at the answers on this previous question regarding the best vehicle on each stage, since distance directly corresponds to coins earned.
(though it doesn't directly answer coins earned over time, which seems to be more along the lines of what you're looking for).
gaming.stackexchange.com/users/4775/Dave McClelland
Moonlander on Moon Level.
Right as you start the level just thrust straight up until you reach about 1/4 on Fuel Tank.
Just release and fall
and you'll end up with 35,000 to 50,000 points within about 20 seconds.
Rinse, repeat.
You'll run about 1 million points every 8-9 minutes.
gaming.stackexchange.com/users/96219/Kyle
Diesel truck in highway can get you easily 1 million per-run (~9000m).
I haven't tried yet but some people report 17000m with the kiddie express, it takes some 33 million to fully upgrade it though (and it's pretty lame before that).
gaming.stackexchange.com/users/92653/donlelek
Kittie xpress Maxed Out on Highway level, 15-20 million coins per round or more.
gaming.stackexchange.com/users/99776/Chris
Go on the moon backwards with the jeep - you get around 300 coins for air time while going on with jeep and when you get in the air hold the break button and you can get up to 3500 coins.
gaming.stackexchange.com/users/99980/o.c.
In Hill Climb Racing, I lack coins. So, in which stage would I be able to gain the most coins by doing tricks and collecting coins left on the stage?
Which stage is best for getting maximum coins?
gaming.stackexchange.com
<hill-climb-racing>
gaming.stackexchange.com/questions/179109
gaming.stackexchange.com/users/24398/Scribblenautical
Try using the Motocross Bike, Moonlander or the race car to gather a lot of coins. There are many ways to farm lots of coins in a single run, such as playing the moon stage.
Community suggestions, regarding coin farming.