I have tried making homemade mayo 4 times and I've had enough... so please do not say it's easy. I have done it in the vitamix, with a whisk, and twice with an immersion blender I paid $60 for just because the first two methods did not work.
Is there a certain brand that is acceptable? I always used Vegannaise but figured there might be a better one out there.
Drizzling the oil in is the key. I watched my grandma make it about a billion times growing up. She just used a handheld mixture-she always told me that the only way to make it right is to DRIZZLE the oil in. If you pour it, you'll F it up.
From Melissa Joulwan's (excellent) Well Fed cookbook:
The Secret to Homemade Mayo (includes what to do if it fails)
Two biggest takeaway points: 1) everything at room temperature, and 2) SLOWLY drizzle in the oil
I couldn't find a commercial Paleo mayo, so I decided to start a food company to make it. Please take a moment to donate or pre-order a jar on Kickstarter:
What specific problems are you having making the mayo? As mentioned in other answers, store bought is made to travel from a production facility, sit on a store shelf, and sit in your pantry. Think about all the extra "stuff" that is needed to preserve something for that long.
Well, I use The Ojai Cook Mayo, LOVE it. Best tasting one on the market. I get it at Whole Foods. I have failed too many times trying to make mayo at home. I do not eat it very often, but when I do I get this brand. They also make Lemonaise. Perhaps it is not the healthiest compared to homemade, but at least it is the best tasting and has better ingredients than most.
In a punch, Veganaise makes an expeller pressed grapeseed one but it contains a small amount of soy as an egg replacement. Wilderness family naturals makes a great mayo based on Mary Enig's 3 oil blend (sesame, coconut, olive Oil) but its a bit spendy. I would buy it in bulk. If you live in Europe, which I'm not gathering, there is an organic brand that uses an olive and sunflower blend but that's all I know of.
I use this recipe every time and it turns out perfect.
I use a light olive oil in my ninja blender. As others have said, a very very slow drizzle of the oil is key.