Others have made the point that a DataSet is not intended to serve as a database system--just a representation of data. If you are working under the impression that a DataSet is a database then you are mistaken and might need to reconsider your implementation.
If you need a client-side database, consider using SQL Compact or SQL Lite, both are free redistributable Database systems which can be used without requiring separate installations or services. If you need something more full-featured the SQL Express is the next step up.
To help clarify though, DataSets/Tables are used in .NET development to temporarily hold data as needed. Think of them as the results of a SELECT query against a database; they are roughly similar to CSV files or other forms of tabular data--you can pull data into them from a database, work with the data, and then push the changes back to a database--but they, on their own, are not databases.
If you have a large collection of items which you need to keep in memory for one reason or another then you might consider building a lightweight DTO (data transfer object, Google it, they're very simple) and loading them into a HashTable. HashTables won't give you any form of relational data, but are very efficient at look-ups.