Paul Jaminet of PerfectHealthDiet.com recommends no more than 1/2 lbs per week of beef liver.
"We recommend consuming in the range 1/4 to 1/2 lb (100 to 200 g) ruminant (beef, lamb, or goat) liver per week for copper, vitamin A, phospholipids, and other nutrients. This eliminates any need for copper supplementation, and provides a great bounty of other nutrients.
If you eat more than ½ lb (200 g) per week of ruminant liver, copper toxicity becomes a real danger. If you intend to eat liver in larger quantities, switch to chicken liver once your ruminant liver intake gets above 150 g or so in a week. Finally, we recommend avoiding pork liver, for reasons we’ll get to in the next (or next two) science posts."
He also recommends that you get any livers from pastured sources:
"We would recommend beef or lamb liver (not pork liver – see the upcoming conclusion to the pork series) from a naturally pastured and fed animal. Chicken liver is also good, but again should be from a healthy naturally raised animal. We don’t normally insist on grassfed for most cuts, but it’s worth insisting on grassfed when you eat liver. The liver is a detoxification organ and unhealthy animals can easily have livers that are rich in toxins and inflammatory molecules.
Supporting that judgment, we have found that grassfed beef livers have a noticeably better taste than conventional livers. Fortunately, organ meats are inexpensive even from organic farmers. We typically pay $4.99 per pound for grassfed beef liver. (Here is the price list of a Massachusetts farm we’ve bought from recently).
Leila’s trick is to soak the liver in milk beforehand, which helps remove things like blood that may contribute to a bad taste."