Matt Bragga was hired by Rice last year. They are having an awful year. 18-23 record with an RPI of 140. I think he can turn them around. He had some strong years with Tech, but also had some rough ones.
I don't really know how they breakdown the coaching staff in terms of duties or responsibilities. Obviously, the easiest one to point out is Belanger, who is responsible for pitching. After that, it becomes a bit more confusing. Most of Fanning's resume seems to be in regards to the outfielders and in recruiting. Guilliams' bio focuses solely on hitting, and I think his role is primarily to be hitting coach. Mingione's focuses just on his head coaching abilities and some recruiting stuff. So, it isn't really clear who teaches infield defense or base running.
Still, I think Belanger has to go. Under Fanning the outfielders haven't been bad, but recruiting may be lacking, but that depends on your philosophy I guess. If he coaches infield then he should probably also be finding a new job.
To replace Belanger, I would look at Jordan Tiegs. I doubt that he has ties to Mingione. However, Tiegs is from Indiana and is currently coaching pitchers at Indiana State. They currently have the 12th best ERA in the country (3.01). Indiana State is 29-9 with an RPI of 41.