Currently I am creating custom tool library in NX9 CAM. Chamfer tool image is attached here.
When I select Chamfer Tool it gives me Target Class - Chamfer Mill Non Indexable and Face Mill Indexable.
When I select Countersinking Tool it gives me Target Class - End Mill Non Indexable, End Mill Indexable and UG 5 Parameter.
Having a brief look at your question I see two possible answers:
If you are a user and don´t want to dig deeper into NX CAM customization, then just ignore the Non Indexable and save your tool in that class.
If you are kind of a customization freak and maybe don´t do this just for yourself, but for a group of people, like to spend some time re-customizing NX on a release change and have fun with sensitive configuration files, then read the NX help article "Add a new tool class". This is not without any future maintenance effort.
I don't understand the question here. Chamfer tools and countersinks are different tool types. If the NX tool type is chamfer mill, select the chamfer mill class in the library. The face mill class is for legacy reasons - before we had chamfer mills.
there is only one option for chamfer tool - Chamfer Mill Non Indexable. Question is - how to define a chamfer mill tool which has indexable insert under target class 'Chamfer Mill Indexable' ?
I presume target class 'Chamfer Mill Indexable' is not available in OOTB NX9
There is no class for Chamfer Mill (indexable) out of the box, even in NX 11. If you want another class, you need to add that with customization (see the documentation). Remember that your customization will require upgrading with each new release, so be sure you really need a separate class.