If we're trying to retain the original rhythms of the melodies, I have two suggestions.
First, you can 'force' the melody into 3/4 by converting each note to the note half its duration plus a dot -- a whole note becomes a dotted half note. This is basically squeezing the 4/4 measure into the walls of the new 3/4 measure. Try playing this a bit to get the feel of the result.
This is the polyrhythmic approach of 4 over 3 and can be heard in Chopin's Fantasie Impromptu, which is normally too fast to catch but is played slowly here. (The piece is technically not in 3/4, but if you consider the triplets in the left hand to be a 3/4 setting you have exactly the same idea.)
That can work, but it's a bit harsh rhythmically and maybe you want to achieve that rolling 'three' feel. For that you can swing a 4/4 into two measures of 3/4, essentially making 6/8, though you can still emphasize the three quarter notes.
If we played Frère Jacques in this manner, we'd have a 3/4 measure with the first four notes played as quarter note, 8th note, quarter note, 8th note. That's like |Ь БЬ Б|Ь БЬ Б| etc. but with 3/4 emphasized (not 6/8). It's a bit unusual but it works, by which I mean that it works musically.
To try to give you an aural example, consider this video of Bring a Torch, Jeanette Isabella and try tapping 3/4 to it, emphasizing "one-and-two-and-three-and" to overcome any temptation to hear it as 6/8. Note: This example is just off the top of my head. If I think of a better example I'll post it (and others are welcome to suggest one).