Perhaps due to the change in Amer Picon's recipe in the 1970's rendering it lower proof we don't really know what this drink is supposed to taste like, however, if you can get your hands on a bottle of the stuff currently available in Europe (e.g through Gerry's of Soho, London) you will not find yourself disappointed. If this is a shadow it's former self, it's still a darn tasty shadow.
Robert Hess has also suggested that Torani Amer is a good substitute for Amer Picon, an experiment the authors have not yet had opportunity to make. If so, you may wish to add a drop of orange bitters to better replicate the taste of the original Amer Picon - or so it's been said Ted Haigh who has tasted the original has advised. Dave Wondrich, as Splificator of the eGullet forums, was able to do a head-to-head comparison against the pre-1970s Amer Picon and various bitters and recommends Amaro Ciociaro as the closest match. Other drinkers in the eGullet thread encourage the use of orange bitters with the Amaro Ciociaro as well.
The truly bold are encouraged to make their own Amer Picon, following the instructions of bartender Jamie Boudreau.
We recommend rye whiskey for the Liberal.
1895 Modern American Drinks by George J. Kappeler
Fill a mixing glass half-full fine ice
1 dash syrup
Half a jigger [1 oz] Amer Picon bitters
Half a jigger [1 oz] whiskey
Mix, strain into cocktail glass
Small piece of lemon peel on top
1935 The Old Waldorf-Astoria Bar Book by Albert Stevens Crockett
Dash of orange bitters
3 dashes Amer Picon
One-half Italian vermouth (stir)