In clause in SQL Query

Another way:

declare @x varchar(100)
set @x='''Viacom'',''Lamar'''

declare @xs varchar(1000)
set @xs = 'Select * from MediaOwners where MediaOwnerName in (' + @x +')'
exec (@xs)

-- one more possibility, if @x members are unique
declare @x varchar(100)
set @x='''Viacom'',''Lamar'''
print @x
Select * from MediaOwners where @x like ( '%'''+ MediaOwnerName + '''% ')

or of course parse the inlist string into separate components
(if you'll allow only a fixed number) and

select *
from ..
where yyy in (@x1.@x2,@x3,...),

How about something like (bear with the typos, I haven't got SQL Server on this machine)

--First create a new (reusable UDF) to split the string up.
CREATE FUNCTION dbo.fnSplitString(@MyString varchar(8000),@delimiter char(1))
RETURNS @SplitString TABLE
(
    string varchar(8000)
)
AS
BEGIN
    DECLARE @chindex int
    @chindex = CHARINDEX(@delimiter,@MyString)
    WHILE @chindex > 0
    BEGIN
        INSERT INTO @SplitString
        VALUES(LEFT(@MyString,@chIndex -1))
        SET @MyString = SUBSTRING(@MyString,chIndex+1,8000)
    END
    INSERT INTO @SplitString
    VALUES(@MyString)
    RETURN
END

-- Then alter your original query thus:
declare @x varchar(100)
set @x='Viacom,Lamar'
print @x
Select * from MediaOwners where MediaOwnerName in (SELECT string FROM dbo.fnSplitString(@x), ",")

Sorry, that last line should have read:

Select * from MediaOwners where MediaOwnerName in (SELECT string FROM dbo.fnSplitString(@x.','))

hmmmm ... wouldn't this work ... just build a TSQL string composed with the appropriate quotes and execute?

declare @MySqlRaw varchar(1000)
SET @MySqlRaw = 'Select * from MediaOwners where MediaOwnerName in (' + ''''Viacom'',''Lamar''' + ')'
EXEC (@MySqlRaw)

(p.s. not sure I have the single quotes balanced in above but you get the idea)

>>wouldn't this work<<
Yes, but it requires using dynamic SQL.  This implies bad performance and lousy security (you must give the user Select permissions for the table).