Crafting this with buckets is far less efficient than using Water Cells. Not only do water cells stack, but you can have a stack of Empty Cells and quickly fill each cell in the stack by right-clicking a water source block. However, cells are more expensive, as it consumes the cell. You can place a Deployer with an empty cell in front of an infinite water source to fill the cells with water. Use Filters to send it more empty cells and to remove the filled water cells, and connect a Timer to all three. Hook it all up with Pneumatic Tubes and you'll have an automated water cell system.
You can run out and spend 5 minutes collecting a whole lot of sand yourself, or if you want to fully automate the system, there are a few ways of automating sand.
Alternatively, you can set up a cobblestone generator and send the cobble to a Pulverizer, which will turn the cobblestone into sand. You would have to filter out the 10% gravel if you use a pulverizer.
However, the most efficient way of getting free sand is by using an Igneous Extruder to produce cobblestone, and then piping that to a rotary macerator. It needs to be supplied with one bucket of Lava and one bucket of Water, but the lava nor the water is consumed. (This is also a great way of setting up a recycler).
So. Now we have a system for a fully automatic Peat farm. But where does it go? You will now need - A Relay, Some Pneumatic Tubes, A Barrel, And a Restriction Tube. Put the Relay on the side of the Turbary. Have Pneumatic Tubes come out of it to the side of the Peat-fired Engines. Then put a Restriction Tube on the end of those tubes. then lead the pipe farther into the top of a Barrel.
To activate, all you have to do is turn on the Engines.