Minion Backup allows you to automatically replce a differential backup with either a full or a log backup.
For example, if you want all of your databases under 10GB to get a full backup in place of a differential backup, then update the MinSizeForDiffInGB and DiffReplaceAction columns in the Minion.BackupSettings “MinionDefault” row: 
UPDATE  Minion.BackupSettings
SET     MinSizeForDiffInGB = 10
      , DiffReplaceAction = 'Full'
WHERE   DBName = 'MinionDefault'
        AND BackupType = 'All';
 
If you want just one database to have this differential backup replacement, first make sure you have configured individual backup type rows for that database in Minion.BackupSettings. For example:
  • DBName=’DB1’, BackupType=’Full’
  • DBName=’DB1’, BackupType=’Diff’
  • DBName=’DB1’, BackupType=’Log’
Then, update the MinSizeForDiffInGB and DiffReplaceAction columns for that database’s ‘Diff’ row: 
UPDATE  Minion.BackupSettings
SET     MinSizeForDiffInGB = 10
      , DiffReplaceAction = 'Full'
WHERE   DBName = 'DB1'
        AND BackupType = 'Diff';
 
For more information on configuring settings for an individual database, see “How To: Configure settings for a single database”.