Plague corpse disposal

With the CDC no longer wasting taxpayer money rewarding people too lazy to defend themselves against disease, new opportunities would exist in the field of plague corpse disposal. As a strong, motivated, red-blooded true American, you need not worry about becoming infected yourself - no dirty foreign pathogen is going to corrupt your precious bodily fluids. But you can earn a living ridding society of the festering reminders of the poor and sickly whom God, in his infinite capitalist wisdom, has seen fit to remove from the society of worthier people.

Witch detector

Despite the infinite blessings of pure capitalism, there would still be plenty of problems in society. And the cause of those problems, of course, is witchcraft. Libruls would claim that lack of rational governance is the cause, but that is only because they too are engaged in witchcraft and wish to deflect blame from themselves. Still, even though the New Libertarian Order would not immediately address the witch problem, it would open up opportunities to enterprising individuals such as yourselves to deal with it and make a tidy profit in the process. Whenever crops fail from incompetent agricultural practices; whenever someone falls victim to a mysterious illness; whenever the weather is unseasonably inconvenient, there will be business for a witch detector.

Reader

Now that the socialist school system has been abolished, and people only learn what they need to jockey pictographic cash registers, you can earn a living as a professional reader for occasions where someone needs all those weird-looking symbols on paper interpreted for them. Granted, literacy is not a very manly or patriotic thing, but as long as you keep it within business hours and don't go around reading any high-falutin' books in public, it's a perfectly decent way to make money.

Bounty hunter

With all those oppressive government police forces out of the way, malefactors can be apprehended in a freer, more appropriate way: By mercenary bounty-hunters armed to the teeth and unaccountable to any civil authority. Sure, you might end up causing more damage to society than the people you apprehend, but what the hell, this ain't France.

Maker of child-sized coffins

In the absence of prenatal care, pediatric medicine, or childcare other than what luck or family inheritance can provide, there will be oodles of little cadavers for the enterprising coffin-maker to serve. Cholera, whooping cough, measles, pneumonia, influenza...all spells big bucks! Grieving parents are a very price-tolerant consumer base, and aren't likely to investigate the particulars of your product - i.e., whether you charge them for mahogany while making it out of plywood. Mo' money, mo' money, mo' money!

Rat catcher / restauranteur

Libruls are always bitching about starving poor people, but watch how crazy they go whenever a rational businessman suggests meeting the demand for food by going to an abundant source of proteins like rats, mice, and insects, among other surplus animals. There would be great opportunities in this domain under Small Government, and given the absence of health inspectors you might also find it worthwhile to vertically integrate your rat-catching / restaurant enterprise with plague corpse disposal, coffin making, and funeral services companies.

Haruspex

Since science and education would become expensive and totally devoted to refining the luxury of the wealthy few, everybody else will need some other way to get weather predictions, medical advice, and relationship counseling. The solution is obvious - Haruspicy! It requires no special skills (other than bullshitting), and all you need is a supply of cheap animals in order to disembowel them and read their entrails - which you could then sell to an unregulated restauranteur and recoup much of your expense. You don't have to worry about sanitation, animal cruelty laws, or being charged with fraud in the Libertarian Paradise.

Orphanage director / pimp

Although the Libertarian Paradise would reject socialist forms of assistance to the needy, nothing would stop individuals from providing it, and in some cases this can be made profitable. For instance, there would be many homeless orphans who would otherwise resort to thievery without a structured environment, food, and shelter. Granted, thievery gives rise to some level of business - i.e., fences - but it also imposes costs on Big Business that cannot be tolerated.

Without police, and being too petty in nature to lead to bounties, we must deal with such thieving proactively with orphanages that teach a good work ethic by providing a highly-demanded service. If owners/operators of commercial orphanages are able to make a profit by selling their children as sex slaves, there would be more market incentive to care for orphans. So, you could kill two birds with one stone, both dealing with a humanitarian problem and upholding the values of capitalism. Take that, bleeding-hearts!

Cemetery / landfill scavenger

In the bustling world of the Libertarian Paradise, a hard-working fellow like yourself could make a living scavenging the metal from bullet-riddled corpses for resale as scrap. With all the gunslingers and bounty hunters around, the supply would be unlikely to dry up any time soon. There are, of course, also gold fillings, rings, metal hip replacements, and various articles of jewelry or surgical implants that might be worth something. And just think of all the perfectly good food and resaleable material that gets thrown into landfills every day! Rather than socialist recycling programs, why not reward enterprising people by encouraging them to rummage through the garbage of their betters?

Faith healer

For the same reasons already stated above, people will be in sore need of medical services - or at least what they believe to be medical services, thanks to the eradication of socialist schooling. Faith healing is the perfect business model: If they eventually recover (doesn't matter how long it takes), their faith in you is affirmed, and they may lavish you with money and free word-of-mouth advertising. If they die, then the Lord has heard their family's prayers and graciously accepted the patient into His Kingdom thanks, in part, to your intercession. You really can't lose, especially in Libertarian Paradise.

Addendum: Integrated Case

For the most enterprising of visionaries, you could create a multi-service, full-spectrum business where most of the above services are provided in an integrated fashion. As a plague victim disposer, you would routinely come upon the orphaned children of the dead and could bring them to your orphanage. Among the children's duties as employees/wards, they would catch the animals both for your restaurant and your haruspex business, scavenge the cemeteries and landfills for money and valuable items, make coffins and other wares for sale, and serve in other profitable capacities as you see fit. In this way, you best affirm the true meaning of liberty, and the heart of Libertarianism: Making other people work for you.

Update: Whoa, ended up on the Rec List when I wasn't looking. Don't you hate it when that happens?