It needs to be a latex enamel, doesn't have to be semi-gloss. The ceiling in my full bath is only 7' and I painted it with Zinnser's PermaWhite satin. That was about 1.5yr ago and it still looks great.
Most any latex enamel [any sheen] will work fine although a bath rm paint is better.
Most any latex enamel [any sheen] will work fine although a bath rm paint is better.