Roller Coaster Airline
This is the nearest you will get to aerobatics. You can check out their website for more information.

Company History
After 11 years of surmounting meticulous procedures and safety
regulations, co-founders Dr. Peter H. Diamandis, veteran astronaut Dr.
Byron K. Lichtenberg and NASA engineer Ray Cronise acquired FAA
approval for G-FORCE ONE, a specially modified Boeing 727-200, to take
passengers on commercial parabolic flights. In August 2004, ZERO-G
flew its first commercial flight operating under the same safety
standards of all major air carriers and established its place into the
extreme tourism industry as the first and only commercial Zero Gravity
flight for the general public.
Additionally, in April 2006, ZERO-G became the first commercial
company to gain permission from the Kennedy Space Center to use the
shuttle runway and landing facilities to operate its weightlessness
flights.
ZERO-G has provided thousands of individuals the opportunity to
experience weightlessness including clients Stephen Hawking, Martha
Stewart and Buzz Aldrin.
ZERO-G not only caters to private clients but various organizations as
well. For example, National Geographic, Nick News and Discovery
Channel have all flown on G-FORCE ONE.
ZERO-G has also been featured on NBC’s The Today Show, Biggest Loser
and The Apprentice.
Apart from commercial flights, ZERO-G also provides research and
educational flights.