A lot of it is just tricking your brain into perceiving one phoneme as another one based on it's environment. Our perception of language is pretty malleable.
I'm not super familiar with vocaloid specifically, but like szumek said you can use "w"s to get an r-like consonant sound, since they're very similar phonetically, and more similar than English "r" is to Japanese "r". But you have to be careful otherwise they'll start sounding like Elmer Fudd lol
For an "r" at the end of a word, it depends on the preceding vowel, but a lot of the time you just blend it with a short "a" at the end, which is a kind of rough approximation of the mouth shape made for rhotics. "u" sometimes works, but that often ends up sounding more like an "l" or "w". These vowels/combos tend to work well for r-coloured vowels:
"nurse", "start" → just a
"north" → o + a, sometimes just o
"here" → i + a, sometimes i + u
"square" → e + a, sometimes e + u, sometimes just e
"cure" → u + a
What works best mostly depends on timing, the complete phrase the word is a part of, and which voicebank you're using. Just play around until it sounds good.