Client Management Suite

Is there a report that I can modify to do this? 

Also is there a way run the "Installed Software by Computer" report, but exclude certain vendors? Ideally I'd remove microsoft, adobe, etc as I am just looking for software that should not be installed. 

you don't mention if you are just talking about the add remove programs table for widows computers

If so its a pretty easy thing.

Here is some SQL to get you started (just make a new SQL report in Altiris)

SELECT
   [vri2_Computer].[Guid] AS [_ItemGuid],
   [vri2_Computer].[Name],
   [dca3_AddRemoveProgram].[DisplayName],
[dca3_AddRemoveProgram].[Publisher],
   [dca3_AddRemoveProgram].[InstallDate]
FROM
   [vRM_Computer_Item] AS [vri2_Computer]
      LEFT OUTER JOIN [Inv_AddRemoveProgram] AS [dca3_AddRemoveProgram]
         ON ([vri2_Computer].[Guid] = [dca3_AddRemoveProgram].[_ResourceGuid])
WHERE

 [dca3_AddRemoveProgram].[InstallDate] > '20150901'
AND
[dca3_AddRemoveProgram].[Publisher] NOT LIKE '%Microsoft%'

I arbitrarily entered a date of Sept 1 2015 you can change that to whatever you want (or set it to be within 30 days of Today which would dynamically update whenever you ran the report/

you would just add additional lines for each publisher you didn't want to see in there like 

AND

[dca3_AddRemoveProgram].[Publisher] NOT LIKE '%Adobe%'

I hope this helps get you started