You can use a lifting "tail" for any plane design but it will depend on the design. The only requirement for a naturally stable flying aircraft is that it must have a reasonably good positive static margin. And for that to happen the rear flying surface must have a lower wing loading than the forward flying surface - this does not necessarily mean downforce though that's an easy way to comply with the rule.
In one extreme case you must use a lifting "tail" or the aircraft would not have enough lift to fly. These are canard planes such such as the Rutan Long-EZ. Now, you may make the argument that the thing at the back is not a tail but a wing. Yes, if you were to insist on classifying planes by rigid categories then the rear flying surface of canard planes are normally called "wings" but this mindset will make one blind to what really happens to aircraft stability as you change the planform design.
CG placement, forces on the tail and planform
The correct CG placement for stability depends on several things including the distance between the wings and stabilizers and the airfoil of the wings but the dominant factor is the relationship between the area of the wings and the area of the stabilizer.
Most full-scale aircraft including ultralights tend to have very small stabilizers:
In this configuration the stable range of CG is usually between the leading edge of the wings and the midpoint of the chord. Typically this manifests itself in the rule of thumb of between 25% to 33% of the chord but for actual values you need to calculate the CG based on your desired static margin.
You will notice that most model planes tend to have larger stabilizers. This is especially true for non-scale models and even more so for free-flight models:
In this configuration the CG for the same static margin (stability) appears to be quite far back. In most cases it is 50% of the chord - right near the middle of the wings. It only appears that way compared to full-scale planes or scale models. Aerodynamically the CG placement gives exactly the same level of stability.
This is when some planes can start to be trimmed with a lifting tail. Some real-world planes with large tails such as the Avro Lancaster may in some conditions fly as if the tail is lifting.
As you increase the size of the stabilizer further the CG for stable flight shifts further back:
This is commonly seen in free-flight duration models. Almost all planes with such planform have a lifting "tail". It is rare to see a real plane with this planform however there is one very famous design where you can obviously see the lifting tail - the Pou-de-Ciel:
(Note that the original design of the Pou-de-Ciel has a catastrophic fault where the rear wing interacts with the downwash of the forward wing - later revisions moved the wing back several inches - DO NOT BUILD THIS unless you know all the issues)
If you change the relationship between the forward and rear lifting surfaces further you will end up with a tandem wing. If you've been following the trend at this point I think you can see where this is going: yes, the CG moves even further back:
The typical CG for tandem wings is completely outside the forward wings and sit between the forward and rear wings. Remember, all the planforms so far including this was calculated to have exactly the same static margin - they are all similarly stable.
All tandem planes have both forward and rear flying surfaces configured to be lifting.
Tandems are less rare in manned airplanes than the almost-tandem configuration above. The most well known is probably the beautiful Rutan Quickie:
As we progress with changing the relationship between the forward and rear flying surfaces we will eventually end up with the canard configuration:
Canards obviously have a lifting rear flying surface. So much so that people instinctively refer to them as "wings". And the CG moves further back still (in relation to the forward flying surface, obviously it is in front of the "wings").
As you can see, weather or not your tail is lifting or generates downforce is not simply a choice you make. In some instances you will be forced to make your tail lifting. In some instances it will depend on your current maneuver. It all depends on the design of your plane.
Side note: Why most planes have (relatively) tiny stabilizers?
There are two main reasons why most designers chose to make the tail small:
First is to reduce weight in the tail. The larger the tail the harder it is to get the weight distribution right for the correct CG. Note however that this is mostly due to most designers using conventional wisdom because as we see above if you make the tail large enough you can shift your CG further back for exactly the same stability.
But this leads us to the second reason: to reduce drag. The larger the tail the more drag it generates. Tandems are the worst-case scenario where both the wings and "tail" generate the same amount of induced drag. However several designers such as Burt Rutan have taken advantage of the characteristics of tandem wing planes to produce very efficient designs.