You'll need to use a splitter function to break your strings down into their individual elements, something like this (not tested because I don't actually have the splitter function on my server):

WITH DBs AS (
    SELECT Item AS DBName, ItemNumber
    FROM dbo.DelimitedSplit8k(@manual_dbname,',')
    )
,   Paths AS (
    SELECT Item AS BackupPath, ItemNumber
    FROM dbo.DelimitedSplit8k(@manual_path,',')
    )
SELECT
     d.DBName
,    @manual_backupdate AS BackupDate
,    p.BackupPath
FROM DBs d
JOIN Paths p ON d.ItemNumber = p.ItemNumber

John