There is DataFrame.to_sql method, but it works only for mysql, sqlite and oracle databases. I cant pass to this method postgres connection or sqlalchemy engine.

Starting from pandas 0.14 (released end of May 2014), postgresql is supported. The sql module now uses sqlalchemy to support different database flavors. You can pass a sqlalchemy engine for a postgresql database (see docs). E.g.:

from sqlalchemy import create_engine
engine = create_engine('postgresql://username:password@localhost:5432/mydatabase')
df.to_sql('table_name', engine)

You are correct that in pandas up to version 0.13.1 postgresql was not supported. If you need to use an older version of pandas, here is a patched version of pandas.io.sql: https://gist.github.com/jorisvandenbossche/10841234.
I wrote this a time ago, so cannot fully guarantee that it always works, buth the basis should be there). If you put that file in your working directory and import it, then you should be able to do (where con is a postgresql connection):

import sql  # the patched version (file is named sql.py)
sql.write_frame(df, 'table_name', con, flavor='postgresql')