Given tables of the following general form:
CREATE TABLE Device
(
ID integer PRIMARY KEY
);
CREATE TABLE EventType
(
ID integer PRIMARY KEY,
Name nvarchar(50) NOT NULL
);
CREATE TABLE [Event]
(
ID integer PRIMARY KEY,
[TimeStamp] datetime NOT NULL,
EventTypeID integer NOT NULL REFERENCES EventType,
DeviceID integer NOT NULL REFERENCES Device
);
The following index is useful:
CREATE INDEX f1
ON [Event] ([TimeStamp], EventTypeID)
INCLUDE (DeviceID)
WHERE EventTypeID IN (2, 5, 7, 8, 9, 14);
For the query:
SELECT
[Event].ID,
[Event].[TimeStamp],
EventType.Name,
Device.ID
FROM
[Event]
INNER JOIN EventType ON EventType.ID = [Event].EventTypeID
INNER JOIN Device ON Device.ID = [Event].DeviceID
WHERE
[Event].[TimeStamp] BETWEEN '2011-01-28' AND '2011-01-29'
AND Event.EventTypeID IN (2, 5, 7, 8, 9, 14);
The filter meets the AND clause requirement, the first key of the index allows a seek on [TimeStamp] for the filtered EventTypeIDs and including the DeviceID column makes the index covering (because DeviceID is required for the join to the Device table).

The second key of the index - EventTypeID is not strictly required (it could also be an INCLUDEd column); I have included it in the key for the reasons stated here. In general, I advise people to at least INCLUDE columns from a filtered index WHERE clause.
Based on the updated query and execution plan in the question, I agree that the more general index suggested by SSMS is likely the better choice here, unless the list of filtered EventTypeIDs is static as Aaron also mentions in his answer:
CREATE TABLE Device
(
ID integer PRIMARY KEY,
Name nvarchar(50) NOT NULL UNIQUE
);
CREATE TABLE EventType
(
ID integer PRIMARY KEY,
Name nvarchar(20) NOT NULL UNIQUE,
[Description] nvarchar(100) NOT NULL
);
CREATE TABLE [Event]
(
ID integer PRIMARY KEY,
PLCTimeStamp datetime NOT NULL,
EventTypeID integer NOT NULL REFERENCES EventType,
DeviceID integer NOT NULL REFERENCES Device,
IATA varchar(50) NOT NULL,
Data1 integer NULL,
Data2 integer NULL,
);
Suggested index (declare it unique if that is appropriate):
CREATE UNIQUE INDEX uq1
ON [Event]
(EventTypeID, PLCTimeStamp)
INCLUDE
(DeviceID, IATA, Data1, Data2, ID);
Cardinality information from the execution plan (undocumented syntax, do not use in production systems):
UPDATE STATISTICS dbo.Event WITH ROWCOUNT = 4042700, PAGECOUNT = 400000;
UPDATE STATISTICS dbo.EventType WITH ROWCOUNT = 22, PAGECOUNT = 1;
UPDATE STATISTICS dbo.Device WITH ROWCOUNT = 2806, PAGECOUNT = 28;
Updated query (repeating the IN list for the EventType table helps the optimizer in this specific case):
SELECT
Event.ID,
Event.IATA,
Device.Name,
EventType.Description,
Event.Data1,
Event.Data2,
Event.PLCTimeStamp,
Event.EventTypeID
FROM
Event
INNER JOIN EventType ON EventType.ID = Event.EventTypeID
INNER JOIN Device ON Device.ID = Event.DeviceID
WHERE
Event.EventTypeID IN (3, 30, 40, 41, 42, 46, 49, 50)
AND EventType.ID IN (3, 30, 40, 41, 42, 46, 49, 50)
AND Event.PLCTimeStamp BETWEEN '2011-01-28' AND '2011-01-29'
AND Event.IATA LIKE '%0005836217%'
ORDER BY Event.ID;
Estimated execution plan:

The plan you get will likely be different because I am using guessed statistics. The general point is to give the optimizer as much information as you can, and provide an efficient access method (index) on the 4-million row [Event] table.