It has been a while since Posit (back then RStudio) dropped support for R versions prior to 3.0.
If you really wanted to install RStudio in a version compatible with R version 2.9.0 you are probably looking at the 1.0 or 1.1 version series. The source code is still available at GitHub - rstudio/rstudio: RStudio is an integrated development environment (IDE) for R - we only offer binary packages of older versions down to the 2021 version (RStudio - Previous Versions - Posit Documentation).
If your use case is to simply replicate some results from back then, I would recommend to consider running the R code outside of the RStudio IDE using command line tools. At the end of the day, RStudio IDE is just an IDE that helps you to efficiently develop code. You always can run R code outside the IDE. Running CLI may be a bit more painful but ideally you should not need to modify your code for replication.
While dealing with the CLI execution is one thing, I am wondering how much information you retained when it comes to R package versions ? Many R packages that exist on CRAN in their more recent versions do have explicit dependencies on R > 3.0.
Maybe you were only using base-R functionality in your codes but if you depend on packages, you should try to ensure that the package versions are installed in the versions as they were back then (R 2.9.2 was released in August 2009) - Unfortunately Public Posit Package Manager at the moment only has snapshots going back to 2017.
Let's assume you have a list of packages and their versions then you also still could be stuck with some of the R packages no longer compiling...
As you can see, this replication exercise could end up being a rather complex task.
Today there is many a tool available for replicating results that include tools such as renv
(R opackage) for package version replicability and docker
for general replication of Software environments (operating system + application software + packages)
When it comes to docker containers, you could for example use the one for r-base
at Docker that at least allows you to use R 3.1.2 as the minimum version.
I would be curious on how you get on with your replication project. Happy to discuss more as needed.