Well, let's see, I know quite a bit about Tengwar and you would need to adapt them, because Dothraki has many sounds that the elvish writing doesn't. It seems the English mode offers better values than the Black Speech mode, because the latter fuses "sh" and "ch" and we could assume that it would do the same with "j" and "zh". So I suggest to use the normal English mode with the addition of fusing k + kh (that is the same tengwar with both over bar and down bar à la "sh" in Black Speech) as the uvular "q". That'd be as close as one could get.
More or less I got: