The US GenWeb Project is a non-profit organization of volunteers that records gravestones found in cemeteries across the United States. This information is recorded to aid anyone doing genealogy research and is provided free. I volunteer for this organization in the State of Washington where I record all information found on the gravestones, as well as take pictures of the stones to preserve for future generations in case the stones become weathered and unreadable. If you would like to volunteer for this organization you can find out how at this website: http://www.usgenweb.org/
While many cemeteries have someone who is recording the stones and information of those buried there, many cemeteries across the country have not had anyone volunteer to record it's informaton for future geneologists to discover.
For information pertaining to Rhode Island, visit:
http://www.brendabova.com/riprovidence/index.html
For a list of all cemeteries in Pawtucket, Rhode Island (Providence County) visit: http://ricemeteries.tripod.com/prov.html
According to the information found on this page, Pawtucket has 9 historical cemeteries of an estimated 10, all of which are large. The US GenWeb Project's volunteers have recorded 22,523 gravestones for their database but the town has approximately 250,000 burial sites. I could not find your grandmother's name listed but there are many Costa surnames so perhaps some of them are related.