Here is an example of a create statement using the default with SQLite CURRENT_TIMESTAMP keyword.
create table user (That is much easier that my previous attempt. Not sure how I missed it. But it doesn't solve the missing now() function for updates. ( did find a language solution for that in Perl but that is for another post). In that case, it will still require the use of datetime('now').
id integer primary key,
username text not null,
password text not null,
created text default CURRENT_TIMESTAMP
Reference: SQLite CREATE TABLE reference.