Can we create a column of character varying(MAX) with PostgreSQL database

If you want to created an "unbounded" varchar column just use varchar without a length restriction.

If character varying is used without length specifier, the type accepts strings of any size

So you can use:

create table foo(   unlimited  varchar);

Another alternative is to use text:

create table foo(   unlimited text);

postgresql postgresql-9.3 sqldatatypes

You should use TEXT data type for this use-case IMO.

CodeHunter