How to implement and tune a LC band-stop filter?
One way to fine-tune a capacitor value is to remember that two capacitors in parallel has an equivalent capacitance equal to the sum of the two capacitors. Two capacitors in series has an effect like two resistors in parallel.

Since you're working with single-digit pF capacitors, the second rule is more likely to help you. For example, 4.7 pF in series with 220 pF gives 4.6 pF. 4.7 pF in series with 100 pF gives 4.49 pF, etc. 

So if you can afford the space of an extra part in series with each of your capacitors, you can trim up the values by choosing the added series cap.
You can also do this in conjunction with Michael's suggestion of using an adjustable trimmer cap to use a trimmer that varies over a large range to produce just a fine tuning effect in your circuit.

Edit

A couple of pieces of advice that you didn't ask about:


Before finalizing this design, be sure to simulated it with part parasitics included. On the capacitor side, Kemet and Murata, for example, are very good about providing parasitic models of their parts. Coilcraft also provides good models for the part family you mentioned.

A little bit of parasitic resistance might actually help your design by broadening out the deepest notches, so making the performance at the target frequency less sensitive to part variation.
If parasitic resistance doesn't broaden out your notch enough to save you sensitivity hassles, consider deliberately adding some small series resistors for this purpose.
Before you finalize the design, be sure to do at least some tolerance analysis. For each capacitor and inductor, do another simulation run with its value adjusted to the maximum or minimum of its tolerance range, depending which you think will mess up the circuit more. If you don't know which is worse, try both. 

If you have access to a tool that provides it, you can tell it the tolerances of each part and it will do a Monte Carlo analysis, meaning hundreds of runs with the values varied randomly each time to let you see the statistical variation of the notch depth, Q-factor, etc.
I was going to mention that for a simulation like you did to give accurate results, you need to simulate it with the actual source and load equivalent resistances it will see in the real circuit, but I see you already did that. For future readers: Don't simulate a filter in a 50 Ohm circuit and expect it to have the same response in a power-supply application with a 1-Ohm load.

In this line I will mention that power supplies are tricky. The 1-Ohm source and 10-Ohm load you simulated are probably W.A.G.'s at best, especially for the 430 MHz you care most about. If the signal you want to block is actually a conducted emission you want to keep from getting off your board, and it comes from digital switching noise, it might be more accurate to model it as a high-impedance current source, rather than the low-impedance voltage source you used.

Uncertainty about the source and load impedance is likely to be a more important source of inaccuracy in your simulation than the layout parasitics.
Testing this circuit will require some thought. For the same reason you can't simulate the filter in a 50-Ohm system and expect it to perform the same in 10-Ohm system, you can't test it with a 50-Ohm source and load and expect the measurement to reflect the real performance.

Of course you can do some reflection measurements to improve your guesses about the source and load impedances (on a board with the filter components un-stuffed). And it might be possible to do some careful math and transform the results of a 50-Ohm test to give the performance in the real system.  

Alternately, on the load side, probing with a low-capacitance 'scope probe (if it has enough bandwidth) will probably give you a more accurate view than connecting through the 50-Ohm coax connections implied by your schematic. Not that the coax connector footprint you drew wouldn't make a reasonable probe test points if you just leave the connectors unstuffed.


I'm assuming this circuit is for a production run of more than 5 units (and it could be 100's, 1000's, or more), because for a one-off you could probably get away with just solder-tacking it out on/over a blank clad board and tweaking it until it works, and save the time and expense of fabbing a PWB.