You might create a blog with informative worthwhile articles that might get search engine ranking and attract people with more general cosmetics, beauty interests, this would be the first stage of the process of attracting prospects, being their helpful friend, then offering products.
Ultimately it take money to make money, whether it is paid content and outsourced SEO assistance to get a site to rank in free search engines results, or targeted paid advertisements. If you venture into paid advertising, Facebook ads might be the easiest to use, don't just push the product, the ads interrupting someone's free time on Facebook should be a bit more friendly, perhaps just offering a "Top 10 beauty tips list" to get them to click, sending Facebook ads to a business page lowers the ad cost a bit.
You can find Private Label Rights (PLR) collections of pre-written articles (10 to 50 in a set) that can help populate a site, search engines don't give you ranking credit for unoriginal material, mixing them with original articles or rewriting would improve the effect.
The marketplace is saturated with Avon reps, the whole idea of MLM systems made more sense before the age of excess media, when you needed neighborhood representatives to get the word out, I haven't had an Avon lady or Fuller Brush man knock on my door for quite some time.
To get a sense for the amount of competition you are facing:
While the Avon parent site has a remarkable 176,000 pages of catalog pages, product reviews, etc.
The domain name where reps are given "their own site" avonrepresentative.com, has some 550,000 pages.
I don't even know if the representative numbers are commonly known or not. The number of pages on avonrepresentative.com who's title mentions the state they operate in include:
Actually, professional internet marketers would not bother with Avon, they could find better paying results for a similar effort without the throng of competing Avon reps., the hot area for marketers are CPA offers in which you are paid a finders fee for delivering a lead, in some cases someone signing up for free trials, these are much easier to secure than hard sales. (you have to pass a phone interview regarding your legitimacy a marketing skills to get into these programs)
(Wanted to mention the alternative, more modern internet specific sales affiliate systems worth investigating.)
Just a couple of current top paying CPA offers in this area:
Lauren Hutton Face Disc $ 45.00 Sale
Luminess Air - Airbrush Cosmetics - 30 Day Trial Offer $ 33.00 Lead
Purity Mineral Makeup $ 29.00 Lead
Sheer Cover $ 17.00 Lead
Magic Minerals - Self Correcting Makeup Powder AsSeenOnTV 2011 $ 6.00 Sale
CosmeticsCentre - Free Makeup & Cosmetics Kit - United Kingdom $ 1.05 Lead
There are also various merchant's affiliate programs that pay a percentage of web site sales, some up to 20%, Amazon, which gets good conversions pays 4% to 8% on common goods, depending on your volume.
If you have created a more general beauty oriented site with a following, you would be able to switch products as needed to improve revenues.