How much do we worry about phonetics? Because we are only going to write and not pronounce, we could create unpronounceable words.
Apart from that, vowels. Do we use a simple system of the 5 classic ones, one from the Romance languages with 7, or maybe 10? Maybe something more complex, like systems of long and short vowels, like in Latin, or nasal vowels. Do we count the English R as a vowel? (It meets all the characteristics.) The same with Y. Maybe we could go for something simpler, like a system of 3, or even just one (that would be funny to pronounce). We also need to think about the use of diphthongs, hiatuses, and triphthongs, and those things, although that already falls under phonotactics.
update:
Remember that we have to make them in such a way that they can at least be written, ergo romanized. Can you use diacritical marks? Like á ä â à (with my keyboard, I can only use those 4 marks).
Update2:
Probably we can just use 6 vowels 'cuz only a, e, i, o, u, and y can have a diacritical mark.
