For this problem, you have to combine two workarounds, one of rhythm, one for pitch. Both will look right and playback properly. I'm going to use a simple example with pictures to help you out.
Rhythm:
Since you need to have dual time-signatures, one time-signature must predominate, in other words, you need to establish the system time-signature for all instruments so the rhythm for all will relate back to that time signature. 6/8 and 2/4 are relatively easy because 2/4's quarter note is equal to 6/8's dotted quarter. Both have two beats per measure, it is just the subdivision that is different. We will use tuplets in 6/8 to simulate 2/4. To do this:
Set a system time signature starting at the bar of the change. (Press T or Create>Time Signature) In this example, we'll use 6/8 as the predominant.
Write out the notes that are in the desired rhythm. In this example just straight 8th notes will do, but any valid rhythm in 6/8 will work.
Write out the notes that are in Violin II in 2/4. To do this, create a quarter note in beat one, then create a duplet (Ctrl+2 or Create>Tuplet...enter 2 in the box). Notice how the quarter is now equal to a dotted quarter in 6/8. Do this for every measure you intend to have in 2/4. Once you have the duplets written, you can go back and edit notes just like normal, just keep in mind you cannot break tuplets. (You shouldn't have to.) Don't worry if the duplet bracket looks funny with the new rhythm, it will be hidden next.
Select the entire part that you made duplets for the 2/4. Go to the Properties window (Ctrl+Alt+P or Window>Properties) and go to the Notes tab. Under Tuplet, change both options to "None" and "No Bracket" That should hide all the brackets. Violin II should now be in 2/4 in everything except name.
Now lets go back and change the time signatures. Select the original 6/8 time signature and hide it. (Ctrl+Shift+H or Edit>Hide or Show>Hide)
Right-click near the now-hidden time signature and create a new time signature for a single staff. (Right Click>Text>Other Staff Text>Time Signatures (one staff only)) Type exactly "6[enter]8" with no spaces. It should render a perfectly good 6/8 text object that you can now position into place. Repeat the process for a 2/4 signature.
Once you have the two text objects we can now position them in place. If you don't have it on already, show all the hidden objects (View>Hidden Objects). Your old 6/8 should show up in a ghost gray. I recommend zooming in a great deal so you can have finer control. Select your new 6/8 text object and position over top of the old 6/8 ghost. If you have magnetic layout on (Sibelius 6), it will make your life much easier by shifting it almost exactly in place automatically. Reseting the position of the text-object is also very helpful if magnetic layout is on. (Ctrl+Shift+P or Layout>Reset Position). It should work with a little patience. Repeat the process for the 2/4 and your done!
Pitch:
Luckily, dual key signatures is far easier than dual time signatures. Again, choose a predominant system key signature to start.
With your new rhythm, set a predominant key signature. (K or Create>Key Signature) In this case, we'll use B-flat major. Note that you may have to adjust your note spacing around the new time-signatures depending on how wide the key signature is.
Create a new key signature again but this time for only one staff. Press K (or Create>Key Signature) and select E major and check the box way at the bottom saying "One staff only." Click it into place on the Violin II part.
Adjust the notes as desired and you're done! Really simply. Sibelius will playback the parts as written so no worries about playback discrepancies.
Hope this helps you out! Let me know if you have any further questions. (I've attached the .sib example file for reference.)
two violins.sib