Why this is difficult.
Jealousy is a natural trait, nearly everyone that falls in love is subject to it at some time. The reason is that the extremely high emotional value of the love interest creates all sorts of effects. Obsessive thinking about them, extreme focus on minor clues of behavior or particular words, cravings for constant contact (holding hands, sitting together touching, arms around each other, frequent kissing, and of course more intimate touching and intercourse).
The negative side of this extremely high emotional value is the fear of loss, and thus a fear of competition, and obsessing on every detail of interaction that might remotely suggest your love interest has any other interest, or any other person might have interest in them.
Jealousy is a form of personal insecurity combined with an active mistrust of the love partner. (Sometimes this is warranted, love can be one-sided and partners may stray.)
It is mistrust to believe they are weak-willed and so selfishly impulsive and superficial they will drop you or cheat on you for a quick lay with someone else, or might even drop you for that.
It is personal insecurity to think your love is not reciprocated, that you are not good enough to hold your partner's interest. This implies they have little commitment and only love you for superficial reasons they can readily find elsewhere; that your qualities are just commodities and your partner is always shopping for a better value -- Somebody funnier, or smarter, or sexier, or kinkier in bed.
This is why it is very difficult to make actual jealousy "cute", it is a manifestation of mistrust and insecurity. And although both may be warranted, when they are not the expressions of mistrust may itself ruin the relationship, no matter how cute you make them. Being mistrusted often results in reciprocation of that mistrust, and mutual distrust breaks the love spell.
Jealousy does occur in most love connections. IMO the best way to handle it is NOT to express it directly, but to have the character struggle with it and find a way to deal with it, to realize their mistrust will ruin them. Perhaps channel it into something else romantic, to reaffirm to themselves they trust their partner and their partner loves them.
How to Represent Jealousy in a Cute Way
In other words, have a self-aware character that understands the stakes and won't surrender to jealousy. It is a conflict they must overcome, which is great for fiction, conflict keeps the reader turning pages. And battling this internal enemy, without revealing their mistrust to their love interest, is something you can do in a cute way. Show their self-talk and self-affirmations, dealing with their insecurities, examination of their own motives and exaggerations of their "competition". People in love are very skewed by their obsession, thus illogical, and that can be funny and recognizable and relatable.
But in the end, I wouldn't express jealousy to the partner. You might get a laugh out of it. In real life relationships people in love get over it, all the time, because forgiveness for an overreaction is something given when in love. But there is a limit, constant jealousy (mistrust and insecurity) is a poison to a love relationship, and can make the mistrusted person feel like a property controlled by the jealous party. That stops feeling like mutual love, and is a recipe for falling out of love.