New, and native answer in 2020

In PostgreSQL, If you only want the current date-time by calling CURRENT_TIMESTAMP() without time zone, and fractional digits in the seconds field which come after the decimal point of the seconds field?

(Tested on PostgreSQL v12.4)

Then use this:

SELECT CURRENT_TIMESTAMP(0)::TIMESTAMP WITHOUT TIME ZONE;

If you define your column's data type as timestamp (not as timestamptz), then you can store the timestamp without time zone, in that case you don't neet to add TIMESTAMP WITHOUT TIME ZONE

Like this:

CREATE TABLE foo (created timestamp NOT NULL DEFAULT CURRENT_TIMESTAMP(0))

In the above function, 0 is passed to get rid of the fractional digits in the seconds field.

I also don't see the problem

Create sample data,

CREATE TABLE foo(ts) AS VALUES (
  now()::timestamp without time zone
);

Display it,

TABLE foo;
             ts             
----------------------------
 2017-09-30 14:25:24.954084
(1 row)

You can see in the above no tz in output. Now let's change to use a with time zone.

ALTER TABLE foo
  ALTER COLUMN ts
  SET DATA TYPE timestamp with time zone;

Here is the output, notice you have a tz of -05

TABLE foo;

              ts               
-------------------------------
 2017-09-30 14:25:24.954084-05
(1 row)

What's your result of SHOW TIME ZONE?

Interestingly though, I do see what you're talking about with,

# SELECT now()::timestamp with time zone::timestamp;
            now             
----------------------------
 2017-09-30 14:27:53.061616
(1 row)

However, we have to know what you're asking.