Hi.
I'll try and offer advice (i am a qualified veterinary nurse)
I would be very careful about chopping and changing his diet, as this could cause more problems in the long run, and he could end up with digestive upsets, It is more adviseable to stick to one diet if he has liver problems, special diets are availble from you vet and i'm sure your vet can advise this.
some times warming the food can help them eat it, (warm dog food smells horrible!) you can try adding chicken or rice as this is quite bland.
Another trick is to leave his food downn for only a set amount of time, if he doesnt eat it, to take the food up and not offer anything else, then offer him the food again later in the day, and only for a set time. as they say a dog will eat when he is hungry.
he might get the message then, . Possibly if he's feeling ill with the liver problem and hnot wanting to eat.
Obviously if he really is not eating well then this could indicate a more serious problem and i would advise you see your vet for further treatment. especially if he is losing weight quickly.. keeping a table of his daily weight may help.
Hope this sheds some light.