The Room of the Immaculate Conception ( Sala dell’Immacolata ) was painted by Francesco Podesti in 1854. These Frescos show images from the proclamation of the Dogma of the Immaculate Conseption by Pope Pius IX.

Painting by Francesco Podesti in the Room of the Immaculate Conception in the Vatican Museum. - Rome, Italy.

It took more research than I thought would be required to find out for sure who the painter was for this image. Having looked at many photos of this painting and ceiling, in all modesty mine is one of the better that includes the ceiling and the painting. This is a high resolution jpg image.
Part of the reason finding out which painting this was, and who painted it was so difficult was that the Room of the Immaculate Conception is adjacent to the Raphael Rooms, and I was doing my google search for a painting the wrong room. Note to self, take a quick snap of the info at the bottom of the photo, it saves time in the long run.

The Vatican Museum
Viale Vaticano
00165 Roma, Italy