Simple phrases:
* Jumpy jaguar
* Jolly jester
* Jazzy jingle
* Juicy jam
* Jumping jack
More complex examples:
* Jonathan juggled juicy jackfruit with joyous abandon.
* Jane's journey to Japan was joyful and jam-packed with adventures.
* The jolly jester juggled jewels, jesting with the jittery judge.
Literary examples:
* "Joyful jays jibber and j**ibber" (from a children's rhyme)
* "Jack jumped over the jacket, and joked about the joyful journey" (from a fictional story)
These are just a few examples to get you started. There are endless possibilities for alliteration using the letter "J"!