[UPDATE: I am leaving this post as originally written with the exception of adding this. While Stockmar may be highly recommended for being great crayons with vibrant color, they are, in fact, MOSTLY PARAFFIN. I found this out after writing this post, and you can read all about my findings, my sincerest apologies, and more here. Stockmar do NOT satisfy the criteria of being either "beeswax" or soy crayons in my mind, as they are only 10% beeswax, 52% paraffin and 30% plant based stearin wax. According to their emails, the Artemis crayons contain NO BEESWAX AT ALL, despite being listed on what I believe to be their manufacturer's site as being "bound by beeswax."]
NO LONGER "HIGHLY RECOMMENDED" - see update directly above
Stockmar

OTHER OPTIONS:
NOTE: I have no personal experience with these "OTHER OPTIONS"- I'm merely reporting my findings of other beeswax and soy brands. Please see the "RECOMMENDED WITH RESERVATIONS, NOT RECOMMENDED and DIY" sections for input on others I have used.

Honey Sticks
These are made in New Zealand of beeswax and non-toxic pigments. Their short, stubby shape is designed to give an easier grip for small hands, and also prevent breakage. I just received email confirmation from Honey Sticks that no other waxes are used, and they are made with 100% beeswax.

Clear Hills Honey Company
USA made beeswax crayons that contain USA made non-toxic pigments and clays. These crayons are made with 100% beeswax.

ÖkoNorm Nawaro Beeswax Crayons
Made in Germany of 25% pure beeswax and vegetable and plant based waxes, these crayons are free of petroleum. They also contain oils and stearine, lanolin, kaolin and organic pigments. These are more readily available in Europe and Australia, the crayons carried by Stubby Pencil Studio are the same crayons, they just have slightly different packaging.

These are made primarily with beeswax, with a little soy wax added and they are colored with food grade pigments. The 8 colors (rainbow + black and brown) and handmade and come in this canvas case.

The general consensus about these crayons seems to be that they make an excellent first crayon for those concerned about children putting them in their mouths. However, the colors and markings are not as great as other crayons, so these are great if your focus is primarily on ingredient safety. They are made with organic soy wax and are colored with organic fruit and vegetable powders. They are also made in the USA.

Artemis Plant Colour Pastel Crayons
According to this Mothering.com review, these are softer than traditional crayons and feel more like an oil pastel. They have natural waxes and plant pigments and are made in Germany.
SEE UPDATE ABOVE! THESE ARE NOT BEESWAX CRAYONS EITHER!

eco-crayons by eco-kids®
These crayons are available in six colors, made in the USA with 25% beeswax and 75% fruit, plant and vegetable extracts.

Earth Grown Crayons on Etsy
These handmade crayons are made of soy wax and are tinted with non-toxic minerals and organic pigments. They come in a variety of shapes, colors and sizes.
RECOMMENDED WITH RESERVATIONS:
Brilliant Bee Beeswax Crayons by International Arrivals

Faber-Castell Jumbo Beeswax Crayons

I have had some parents contact me and say that they love these crayons, and they are more affordable than some of their competitors. However, I have been in contact with Faber-Castell and they have not been very forth coming with their ingredients, but at least they responded, unlike the the maker of the crayons directly above. The most I got out of them is that they are made in China, the beeswax is sourced in China, and "the additional raw materials are palm oil based," but they do not contain petroleum/paraffin. Something to consider is that like petroleum, palm oil comes with its own set of environmental issues like deforestation and the consequential diminishing orangutan population. When I inquired about the pigments, I was told, "I am unable to provide that information as it is proprietary."
NOT RECOMMENDED:
Crayon Rocks®

A great concept, but besides the fact that these need to be used with older children because they are a choking hazard (despite that they are designed to fit in very small hands), they are not impressively vibrant, and most importantly, these have been the least durable crayons we've owned. I swear if you look at them wrong they will break! In a matter of a few months we were left with nothing but shards. Maybe if you had a much older child who could take good care of them, but again, these are very small so I'm not sure how ergonomic they'd be for a larger child.

Clementine Art Natural Crayons
These soy crayons had great color, but again, broke very, very quickly. Not durable and in my opinion, not worth the money. They also make crayons in a rock shape, but given my experience with their brand as well as rock shapes of another brand, I'd be very skeptical about those as well.
P'Kolino

DIY:
For those willing to try making your own, Wee Folk Art has a great tutorial. I ended up having to make similar adjustments that are noted in the comments. Unfortunately, it was long ago so I can't remember exactly what I did, but I believe it was that I had to add a little bit of water to hold the emulsion. They came out decent, but I had to wait to use them until my daughter was a little older (she was only a year old) because they were harder than store bought crayons so you needed to apply more pressure. I already had beeswax on hand, and any number of things can be used for molds, but I purchased this mold and it was very useful. I figured it could be used for homemade candy in the future. I didn't want to spend anymore money, so I used my mom's food dyes from her large collection for cake decorating. However, there are natural pigments and dyes available if you're interested. This is the photo of our results.
