There is no software for calculation of bird diversity. You have to do it manually & analyse the data by using diversity indices software or by using formulas manually.
There are a lot of tools from statistical software (eg R) to geographic information systems (like Quantum GIS), the decision is depending heavily on the questions of your study.
However there are also specific tools for bird count data, they can be found here:
As Prabhakar Ramchandra Pawar said, you have to compute diversity indices in order to determine the bird diversity of the area. These diversity indices can be calculated using a wide range of available softwares such as R-software package, GENStat etc.
There are several software which could be used to estimate diversity indices. You may use the freely available software like Biodiversitypro, PAST or EstimateS. If you are used to R , then the Biodiversity R package will be of use. Using the known formula, you may also calculate these indices on microsoft excel.
Any statistical program will do this for you but R is good because it is free and easily accessible. A number of studies are currently using it for bird count data so it is easy to follow their methods.
Depending where you are you may also want to look up ebirds.org which could aid in giving supplemental data. There you will find different data concerning various species and you can also have frequency graphs for certain time periods.
If you are interested in estimating trends from bird count data, you could use the TRIM program, and even better is BirdStats, which works with TRIM from Access: