While this functionality is not built into the CMSContext properties, it's shouldn't be too hard to adapt from some of the documentation.
First, you'd need to select all the sibling nodes:
using CMS.SiteProvider;
DataSet ds = null;
// create a TreeProvider instance
UserInfo ui = UserInfoProvider.GetUserInfo("administrator");
CMS.TreeEngine.TreeProvider tree = new CMS.TreeEngine.TreeProvider(ui);
// get dataset of tree nodes specified by alias path and class names (separated by semicolon),
// the second parameter says whether to return default culture documents if the required
// document language version is not available
ds = tree.SelectNodes("CorporateSite","/Products/%", "en-us", True, "cms.menuitem;cms.products");
// do something with dataset ...
The trick here is to just use the path "./%". This will get all the documents under the current parent document.
Then you would just have to parse them to find where your current document is in the DataSet. After that, you can get the previous and next items.
Hope this gives you a starting place.
If you have any more questions, feel free to ask.
-Eric