Kate,
Industrial vinegar is one trick that some people use. Mix in a little Dawn dishwashing detergent and you'll increase the potency. This is a contact herbicide so you have to treat the liverwort and not the surrounding plants.
When the plants are actively growing Round-up will work on them too but it would be VERY slow this time of year. Again it is a contact herbicide so paint the liverworts or use very directed sprays.
Good luck!
Kevin
