I rent cars when I drive. Is there any liabilty insurance policy that
will cover a person who only rents cars so that they don't have to pay
the highly over priced liability insurance that the rental car
companies so willingly offer?

I not posting this as an answer because you will probably have to call
around among insurances companies to find a policy that is suitable
for you, but, according to various published sources, such liability
policies are not uncommon at an annual cost of a few hundred dollars.

Here are links to a couple of those references:

USA Today: Do you really need car rental insurance?
http://www.usatoday.com/travel/columnist/mcgee/2004-03-09-mcgee_x.htm

Kiplinger.com: Insuring a Car You Don't Own
http://www.kiplinger.com/columns/ask/archive/2005/q0117.htm


I checked the Geico and Allstate sites and discovered that their
online quote service does not work with this kind of a policy, so, as
I said, you will probably need to call an insurance company or an
independent agent to get more information on coverage limitations and
a quote.  Also, beware that such a liability policy will not cover
collision damage to a rental car.

Believe it or not, there are really two separate questions here.  The
first question involves an insurance policy that will fix the actual
car when damaged, and the second question involves fixing your bodily
injury.  You can buy a policy for hired and non-owned autos only. 
Just call an independent insurance agent somewhere in your area. 
You'll have better luck with an independent agent than you will a
captive agent like AllState or State Farm.  They will need to know
approximately how many times per year you rent and how many miles you
drive per year (obviously just an estimate).  The policy shouldn't
cost more than $500.