The oscillator modules from Sparkfun you are linking to are not meant for RF transmission. You need a transmitter/receiver pair for each parking spot, assuming you are mimicking a system that would have distances of more than 3 feet. A Sparkfun module that you might look at is: RF Link Transmitter - 434MHz WRL-10534. In a simple minded system you could use transmitter/receiver pairs with four different frequencies. If all there spots were close to each other but far from the entrance, you could use one transmitter/receiver pair with different codes for the spots.
In the title of the question you use the phrase "power multiple LEDs". I assume you are not literally powering the LEDs, but signaling them.
For the very short distance in your model, I do not think much of an antenna would be needed.
Shortening an antenna from its ideal length is not a problem providing you accept and possibly counter the limitations that shortening brings. Here are some words from this site that tell you the story: -
A shortened dipole is simply a dipole antenna that has been shortened.
Since it is shorter than its resonant length, it will not be resonant
and will exhibit both resistance and reactance at the feed point.
Shortened antennas tend to have a capacitive reactance and therefore
need an inductance to cancel the capacitance and bring the antenna
back to resonance. Normally the resistive impedance also drops as the
antenna is shortened, so additional impedance transformation will be
needed to effectively match the antenna.
A shortened dipole will act similar to a full sized resonant dipole in
many ways. The effect of ground will still be important, current will
be maximum in the center and very close to zero at the ends with
maximum voltage at the ends and minimum in the center. If the antenna
is center fed, it will still be balanced, with equal voltage and
current distributions on both legs.
From the principle of conservation of energy, we know that if we can
feed energy into an antenna, it will radiate. We also know that with a
suitable matching network, we can feed power into nearly anything,
including a shortened dipole.
The article goes on to demonstrate how the impedance of the antenna becomes reactive and how the idealized "50 ohm" input resistance becomes significantly less when shortening is done excessively.
Here is another excellent site that explains you can make an antenna from any length.
In short, any length works providing you can get the power into it that you require for transmission. Reciprocity means that a badly shortened antenna works just as "inefficiently" as a transmitter and receiver. There is no silver bullet of length - optimum is quarter, half and full wave antennas but don't let this stop you running the antenna at significantly shorter lengths.
One caution - if you are wanting to transmit several hundred milli-watts or above, not having an ideal antenna (proper length or compensated by matching networks) you may damage your transmitter output stage.
Best Answer
The standard way to tune things is with a varactor.
Although a typical varactor can achieve more than a 4:1 variation in capacitance, once that's embedded in a circuit, including bias, parasitics and a corresponding inductor, you rarely see the hoped-for octave tuning range. Replace the inductor with antenna elements and you'll see even less than one octave.
You can get varactors in capacitance ranges and packages appropriate for frequencies in the order of MHz to GHz. However, I've often had a hankering to test very high-K ceramic capacitors like Y5U to see what the 'varactor' performance would be like at very low frequencies indeed.
You would need to restrict a transmit antenna to very low power levels to use voltage controlled tuning, as the RF voltage would modulate the tuning, not a problem with a receive antenna.
You may need to use several varactors, to tune both the antenna and the matching network to the feed. It will not be a trivial or 'cookbook' task.
Digital tuning may be easier to use, where you would use hard switching to change the physical lengths of antenna elements. Historically, PIN diodes have been used for this purpose. At low enough frequencies (<100MHz), you could even experiment with the humble 1N4148 (not a PIN) to get a feel for what can be done. Silicon on sapphire CMOS switches are a modern alternative RF switch, easier to bias than diodes, and capable of handling some quite impressive powers, look for 'CMOS RF switch'.