ingenious.....here ya go!
when you type, you must watch and make sure the proper character is displayed!
I = イ
N = ン (You need to type N 2 times)
JI = ジ
NI = ニ
O = オ
U = ウ
SU = ス (Su because there is no s、And the u is silent in this case!)
THI = ティ (I think it could be written as shi as well because the i might be silent in conversation but more on this later)
N = ン
KE = ケ
RU = ル (Again, there is no r )