The names Rühle/Ruehle do seem to be a bit more common in Germany than Ruhle. On the other hand, if your ancestors spelled their surname Ruehle there was no reason to change it, and if they spelled it Rühle they would most likely have transcribed this as Ruehle right upon entering the country. (PS: But as hobbs pointed out in a comment, it’s quite possible that someone else with no knowledge of German transcribed the name from German passports.)
For now, let’s assume the original name to be Ruhle without the umlaut.
What you want is probably not an accent-free German pronunciation but an English one that is conscious of the name’s origin. That would be like the English word rule, but with the final e pronounced (without giving it any stress). Sort of like pronouncing the words rule export, stressing the first word, and stopping right before the x.
Now if the original name was Rühle, after all, then only the quality of the u sound would be different. Since most native English speakers can neither produce a proper ü sound nor hear the difference, you needn’t worry about this. But if you can speak French, it’s almost exactly the same as the French u sound, as for example in sûrement.
By the way, ë only appears in German in the same way and for the same reasons that some people write the English word co-operation as coöperation. (The only exception is Luxembourgish, which might be called a national language that is also a German dialect. In Luxembourgish orthography, ë denotes a sound somewhere between e and ö and is transcribed as eo when the letter is not available. But this is not relevant to your name as it has no common variant of this kind.) It is conceivable that upon entering Australia your ancestors might have changed the spelling of their name to Ruhlë in order to indicate that the last syllable should be pronounced. But even this doesn’t seem very likely.