I have a sqlite (v3) table with this column definition:
\"timestamp\" DATETIME DEFAULT CURRENT_TIMESTAMP
The server that this database live
In the (admitted rare) case that a local datatime is wanted (I, for example, store local time in one of my database since all I care is what time in the day is was and I don't keep track of where I was in term of time zones...), you can define the column as
"timestamp" TEXT DEFAULT (strftime('%Y-%m-%dT%H:%M','now', 'localtime'))
The %Y-%m-%dT%H:%M part is of course optional; it is just how I like my time to be stored. [Also, if my impression is correct, there is no "DATETIME" datatype in sqlite, so it does not really matter whether TEXT or DATETIME is used as data type in column declaration.]