I am going to put my two bits into this question also.
There are several existing colored absinthe on the market at the moment and a couple of ways to get various colored varieties. Artificial coloring is the most common.
Absinthe may be found in the following colors: Green, Red (or Rose), Yellow, Brown, Clear and Blue.
One way to get the desired colored is to make your own absinthe as can be seen in the following recipe.
Put the dry herbs in a large jar. Dampen slightly. Add 800 milliliters of 85-95 percent alcohol. Wine spirits make a better product than pure grain alcohol. Let steep for several days - a week is better - shaking occasion absinthe. Then add 600 milliliters of water and let the whole macerate for another day. Decant off the liquid squeezing as much from the mass of herb as possible. Wet the herbs with some vodka and squeeze again. Recipe should give a little over a liter and a half of green liquor. It must then be distilled... - Traditional absinthe recipe
There or other non-traditional herbs and artificial coloring agents that are used to make a particular color also.
Absinthe can be classified differently
Green absinthe – classically natural color of absinthe. Color can vary from deep emerald to light green or olive shade. Practically every manufacturer produces green absinthe. But because the natural dye (chlorophyll from the leaves) is not durable therefore manufacturers in most cases use artificial coloring. To preserve natural green color of absinthe it is bottle in green or brown bottles.
Yellow absinthe – is usually natural colored because natural dye from chlorophyll has a tendency to lose its color and become more yellowish in couple of months after production (aging of absinthe).
Red absinthe – is colored by extract of pomegranate or macerated with blossoms of hibiscus what gives absinthe light-ruby shade and original after-taste. But nowadays majority of red absinthes are artificially colored.
Brown absinthe – unlike all the other absinthes this kind is macerated with the roots of wormwood not the leaves of blossoms. Also dark color can be achieved by adding black cutch extract which brings slight flavour of berries. - Kinds of Absinthe
Wikipedia has this to say about absinthe:
Absinthe may also be naturally coloured pink or red using rose or hibiscus flowers. This was referred to as a rose (pink) or rouge (red) absinthe. Only one historical brand of rose absinthe has been documented.
Many contemporary absinthe critics simply classify absinthe as distilled or mixed, according to its production method. And while the former is generally considered far superior in quality to the latter, an absinthe's simple claim of being 'distilled' makes no guarantee as to the quality of its base ingredients or the skill of its maker.
Blanche, or la Bleue: Blanche absinthe (also referred to as la Bleue in Switzerland) is bottled directly following distillation and reduction, and is uncoloured (clear). The name la Bleue was originally a term used for bootleg Swiss absinthe, but has become a popular term for post-ban-style Swiss absinthe in general.
As noted in Montijello's excellent answer, clear absinthe may be easily artificially colored.
There are a variety of Clear Absinthes on the market as can be seen on the following website:
This is usually the favourite of people trying absinthe for the first time, and of the most experience absintheurs: where absinthe drinkers settle again in the end, having explored the world of green absinthe. Quite simply because it is balanced and delicious. Much of the finest absinthe is clear. Also known as Blanche, La Bleue, and white absinthe...