I dont know why you are having pick up issues even after CNG tunings. Ideally you should get 120+ Km with AC in city conditions over a 60L cylinder (8.5 Kg CNG). That is a good mileage for a 1300cc car.
Acceleration issues can be due to many reasons, like (troubleshoot in this order with any good mechanic):
-- Incorrect selection of Spark Plugs, invalid gap, fouled plugs, pre-ignition etc.
-- Faulty Plug Wires
-- Incorrect Air/Fuel Mixture
-- Air sucking into Venturi and into combustion chamber
-- Faulty Advancer or not functioning consistently
-- Wearing or degraded coils
-- Choked AC condensor also sometimes makes excessive slight load when AC is ON
-- Throttle Body issue
-- Valves issue
-- Can be many other things, but cant get in my mind right now if its running fine over Petrol...
I have three 07/08 LIANAs in my direct friends circle, and each of them runs perfectly fine over CNG including mine.
If you have an after market CNG kit, any good mechanic can tune this for you then, not a big issue.
Let me know if you are having problems in finding a good mechanic here in Khi, I will refer you to someone.