One option would be to use a Japanese R. Although it would sound accented, this is still the natural pronunciation of R for some English speakers, and it can still sound good depending on the specific words and context.
Another option is to use W (eg. wa wi we wo). The English R is commonly an approximant consonant, and W is also an approximant consonant. Pronouncing R as W is also natural for some English speakers.
A trick you can also use is making a very short "u" note before the main note, and editing the properties of the "u" note to have a high g flag (eg. g+30).
These techniques are not one size fits all, so you should experiment with all of them and see which one suits each specific word you're working on.