That's the tough one....
We are talking about very simple devices where each stage does more than
one task making it difficult to setup so some luck is required as well.
I've built tons of FM transmiters and sometimes it's better to put the
"misbehaved" unit away and simply make new one. Usually they
work very decently or stable enough if you follow few simple rules.
One thing to remember is that stable oscilator needs good quality parts,
all connection should be as short as possible (in my case all components
are sitting tightly on PCB and the PCB is ca 25x15mm or 1"x5/8"),
do not expect oscillator to work too hard to get the bigger range.
The more you load it, the less stable it is. Add another stage to boost
signal if required. For example most od the simple FM transmitters
use small capacitor as feedback from emitter to collector and emitter
is connected to battery through resistor. Don't just lower the value of
that emitter resistor and don't increase battery voltage too much.
You might get biger range but terrible stability. Use transistor with
higher gain. The bigger the better... Just remember we are not talking
about gain at audio frequencies, we need transistor with good gain
for operation at ca. 100MHz. The bare minimum is to have transistor
that can oscillate at 300MHz. Make sure not to cook components.
Transistors are very sensitive to temperature and with so short
connections they will be stressed thermally. Even though they don't
nececarily burn and they still work, thermal shock will reduce gain to
some extent - and we don't want that to happen. So before soldering
try to make sure that wires are clean (scrape the surface with the knife
if you have to) so that soldering is as fast as possible.
Capacitor in the circuit should be ceramic and have black tip.
Coil should use a bit thicker copper wire, not that tiny 0.2mm diameter
enameled wire you took from wallwart (remember "skin effect"). Try to use
0.6-0.8mm diameter (or even 1mm).
Once you have whole thing tuned the way you like it, you might want
to seal it with wax or similar so the LC circuit is mechaically more stable
and less sensitive to ambient air changes (temperature, moisture).
Add voltage regulator for the oscillator, decoupling caps etc.
And don't use that mickey mouse FM reciever from dollar store for testing.
Maybe problem you experience is not transmitter related.
My priority was always stability and then then range so 9V transmitters
with two transistrs would only occasionally break 300-400m range
without antena on transmitter (and this is in open). On the other hand,
they work quite nicelly (installed in pastic box because of missing antena,
all transmitted energy comes from coil, very little drift with temperature
and proximity of the hand or body).
For example unit sitting on the desk will drift so little after placed
in shirt pocket that no adjustment on receiver is required.
My advice is to use best judgement and experiment, build many and
keep the good ones for yourself (unfortunatelly they don't always come
out the same even if you have same PCBs and same batch of components).
Wish you luck...