What is the difference between cough up and fork out in term of paying unwillingly
"To fork over" is also common. The three are commonly used in the USA. I see no difference. Be aware that they are often used humorously without any intention of insulting or offending.
Jack, you owe me a dollar for the coffee. Fork it over.
I had to cough up $100 to pay for the mechanical work on my car.
Jill, how much did you fork out for that coat?