According to their contract each teacher is allowed to take off two days each year for religious reasons.
The Washington Post said the reason given for the refusal was because 'religious observance obligations require attendance at religious services held during the school day.'
The main Good Friday service is always at 3pm.
The day is not officially a national holiday in the United States, however some states including Florida and Texas have made it a holiday and the stock markets are closed.
Teachers also noted that the district had already added six more snow days than originally planned for the year after bad weather.
The Cranston Teacher's Alliance is suing the district, which had approved a 2014-2015 school calendar that kept schools open for religious holidays, which was a change from the previous year where schools were closed.
Cranston Teachers' Alliance President Lizbeth Larkin made a statement criticising the decision. She said: "If the Cranston School Committee wants to open schools on important religious holidays, they must honour and respect their employees' religious beliefs.
"I wish they had not opened school on the Jewish Holy days and Good Friday, but since they made that decision they should not be telling Christians of all denominations that Good Friday is not important enough to merit a religious leave day."
The Cranston School Committee and Superintendent Lundsten issued a joint statement. It said: "It is unfortunate that the Cranston Teachers' Alliance initiated a lawsuit regarding Good Friday.
"Certainly, we always seek to respect our students' and staff's religious practices.
"From our perspective, this is about a calendar that was agreed upon and passed by the school committee nine months ago.
"Teachers, teacher assistants, technical assistants and bus aides have the provision in their contracts to request up to two religious observance days.
"The contractual language states, they may be granted the day off if their religious observance obligations require attendance at religious services held during the school day."
The issue is ongoing.
