It depends on what you are trying to restrict.
In general, publicly accessible API is not restricted. However, as long as you don’t grant the untrustworthy code the ReflectPermission("suppressAccessChecks") permission, it won’t be able to get access to non-public API in another package.
If you have a list of packages to which you want to restrict all access, there are two steps. First, in the Security properties, include the restricted package in the package.access list. Then give your trusted code RuntimePermission("accessClassInPackage." + pkg).
A common way to distinguish your untrusted code is to load it from a different location, and refer to the different codebases in your policy file when granting permissions.
The Java security architecture is very powerful, but I know it is also complicated; if you would like a more concrete example, please describe exactly what calls you want to restrict and I’ll try to be more explicit.
To do what you want without modifying the java.policy file and/or the java.security file would be very difficult, maybe impossible. The java.security.Policy represents the information in java.policy, but it doesn’t offer write access. You could create your own Policy implementation and install it at runtime as long as any existing SecurityManager permits it.
On the other hand, you can specify a custom java.policy file as a command-line option. If you are providing a complete application with some sort of launcher, that might be easily accomplished. It also provides some transparency to your users. A sophisticated user can review the permissions you’d like to have granted to the application.