At the risk of talking to myself here, I thought I would update my message with some new findings for my great-grandparents Michael Tierney and Annie McDonald.
In order to at least find a secondary source for Anne's maiden name I ordered her son Thomas' social security SS-5 which did have her listed as "Anne McDonald." You can see an image of the form here:http://www.flickr.com/photos/johnjt/4927285242/
I also found her death certificate which confirms McDonald as her maiden name and has her parents as Michael McDonald and Anna Dougherty.
I also was able to acquire Michael's NYC police transfer and assignment card and have confirmed his death date plus found several others.
On the police force: 8/4/1886 - 3/10/1913
(Death date is on a different card from the NYPD than the one linked below.)
You can view the card here:http://www.flickr.com/photos/johnjt/4926751567/
Based on the naturalization date of the NYC Police card I was able to order his naturalization record, but alas, in 1885 they did not take down more than basic information and so still have no detail on where he emigrated from in Ireland.
I know nothing about other possible family in NY or elsewhere, so I'd be very glad to hear if anyone thinks they might have family related to Michael Tierney and/or Anne McDonald.