According to the webpage at
http://www.flaherty.ruoffonline.com/html/flaherty.html
"MARK FLAHERTY (? FLAITHBHEARTAIGH) was born 1847 in Inis Meain, County Galway, Ireland, and died 1935 in Woburn, MA. He married SUSAN HOWLEY January 08, 1870 in Woburn, Massachusetts, daughter of PATRICK HOWLEY and ANN O'CONNOR. She was born March 1848 in County Clare, Ireland, and died 1923 in Woburn, MA."
A good starting point is to locate Susan's 1848 baptism among the many RC church records now transcribed. There is a corner of Clare around Lisdoonvarna that is in the Diocese of Galway, not fully transcribed or with records dating later than 1848. If that's the problem, then plan B is to contact either the RC church in Woburn for Susan's marriage record (which might state a former Clare parish) or use the "American Ancestors" RC churches of the Boston area at NEGHS, online free for indexing or by subscription for full images.
With Susan born in Clare, her younger sisters might have been too, in which case you can try their marriage records as well. Then try their obituaries in case a Clare location is named in those. Remember to check for any later-in-life trips back to their Clare home area.
This sounds like a fruitful search effort, because Howley and Droney are not numerous names like McMahon and O'Connors. For the latter, Andrew is not overly used so it might be useful to explore anyone naming a child Andrew O'Connor(s) prior to 1850 in Clare.
I checked the Library's New England Naturalization database (donated records section, emigration) for your surnames but saw nothing useful. However, there are other naturalization records for the Boston area that could be consulted in record offices (NARA, MA State) that may be digitized by now, and I believe that newspapers of the 1800s also printed long lists of who had been naturalized.
Finding other descendants of the Howley sisters may also be helpful. I found the above one by Googling.