Humm that's a tricky one as jorose said, she may have been in transit in Liverpool. This is probable as her last known residence is given as Ireland, not Liverpool. Then again, why didn't she travel from Queenstown, or was Liverpool closer? However there are a few things you can do if you think she stayed in Liverpool.
You may already have these:
This is the only record of an Anastasia Sullivan: is she the same as yours?
First Name: Anastasia
Last Name: Sullivan
Ethnicity: British, Irish
Last Place of Residence: Callan, Co Kilkenny, Ireland
Date of Arrival: Apr 25, 1921
Age at Arrival: 17y Gender: F Marital Status: S
Ship of Travel: Celtic
Port of Departure: Queenstown
Manifest Line Number: 0003
Manifest page 229
Anastasia Sullivan 17 F S Occ Housemaid Read: Yes/English
Country: Ireland
City or Town: Callan Co Kilkenny
Father: John Sullivan, Kilkenny, Callan Co Kilkenny
Destination: NY New York
Here's Stasia Sullivan:
First Name: Stasia
Last Name: Sullivan
Ethnicity: British, Irish
Last Place of Residence: Thurlow Co., Ireland
Date of Arrival: Jul 16, 1922
Age at Arrival: 19y Gender: F Marital Status: S
Ship of Travel: Adriatic
Port of Departure: Queenstown
Manifest Line Number: 0007
Page 460
This sailing she is struck off the manifest - seems to have been going to
Friend: James Penny 128 Como Ave Buffalo NY
Here she is later the same year:
First Name: Stasin
Last Name: Sullivan
Ethnicity: Gt. Britain, Irish
Last Place of Residence: Boaladuff, Ireland
Date of Arrival: Dec 18, 1922
Age at Arrival: 19y Gender: F Marital Status: S
Ship of Travel: Baltic
Port of Departure: Liverpool
Manifest Line Number: 0006
This time James Penny of Buffalo is noted a brother-in-law.
Length of term always 'term' written in with something which I believe reads 'indefinate attached to her.'
Been in states before: Yes
5ft 1 fresh complexion, fair hair, grey eyes
Unfortunately manifests give destination rather than departure addresses - unimportant for them, but interesting for us
If Anastasia did stay in Liverpool for a time, I wonder were Penny in Liverpool? Might be worth looking for PENNY or SULLIVAN in Liverpool Directories?
Historical directories
http://www.historicaldirectories.org/hd/index.asp - only goes up to 1910's but might be worth a try. There are Gore/Kelly's directories for 1920's try asking or looking at Resources on Lancashire board.
Even 1911 census might show common links which might give you clues.
Also if you know James was in States in 1920, if you haven't got access yourself, go to USA board and ask someone to look for your James Penny. That way you'd have an age and be able to say which if the James Penny on Ellis Island site was him.
Also, as James seemed to have married sometime between July and December 1922 (unless 'friend' was a mistake)- have you looked for his wife, Anastasia's sister? Presumably she crossed from Ireland too?