Some of the attacks were deliberate, such as the Islamic State group using bulldozers to destroy the ancient Saint Elian Monastery in Homs province in 2015. The majority, however, were caused by front-line combat, shelling or rockets.
Around half of all Syrians are now either internally displaced or have left the country.
The group, which collects statistics on the war, said government forces were responsible for 60% of the 124 documented attacks since fighting erupted in March 2011. The rest were blamed on IS militants, the al-Qaida-linked group Hayat Tahrir al-Sham and other factions of the armed opposition.
There was immediate comment from the government, which rarely comments on reports from foreign organizations.
"Targeting Christian places of worship is a form of intimidation against and displacement of the Christian minority in Syria," said Fadel Abdul Ghany, the founder and chairman of SNHR.
The report said IS was behind 10 attacks on Christian sites, five of which were in the northern city of Raqqa, once the extremists de-facto capital. The group was known for displacing and killing Christians in areas it controlled and confiscating their properties.
Hardest hit was the northern province of Aleppo, with 34 attacks, 24 by rebels and six by the government.
The highest number of attacks by government forces — 27 out of 29 — was in the central province of Homs.
SNHR's report also placed blame on Syrian government allies Russia and Iran, but did not specify how many of the attacks they'd caused.