So yes, you could flip a coin 256 times and copy down the results into a 256 bit number and as long as your number is less than the (prime) number p shown above it is a valid private key.
A coin is a really bad source of entropy though.Use 512 coins, and drop them from a height. Unleash a dog/kid into the room to scatter and or lose some coins. Then pick up 256 coins randomly
