The Nurse demonstrates love to Juliet by working to make Juliet laugh, keeping Juliet's secrets, and looking out for Juliet's best interests.
Readers see the Nurse make Juliet laugh in both Act I.iii and Act II.v. In the first act, the Nurse teases Juliet about when she was weaned as a young toddler. She tells a tale of Juliet falling down, during which the nurse's husband had warned Juliet that one day she would "fall" for a man. The play on words relates to the discussion they are about to have regarding a potential marriage to Paris.
In Act II, the Nurse returned from speaking with Romeo about Juliet's marriage to him, and she just kept changing the subject avoiding actually answering Juliet's questions about what Romeo said. This playful banter in eventually overcome, but the purpose served is to build humorous supense. This playing relationship can only happen between people who honestly love each other, otherwise there would be no forgiveness for teasing.
In the same scene from Act II, the Nurse demonstrates that she will keep Juliet's secrets because we never saw her stop to tell Juliet's parents, and she slyly brought a rope ladder so that Romeo could sneak into Juliet's room that night. Throughout the rest of the story, the secret romance is never revealed to anyone by the Nurse.
Next, Juliet seeks the Nurse for counsel:
How shall that faith return again to earth(215)
Unless that husband send it me from heaven
By leaving earth? Comfort me, counsel me.
The Nurse offers counsel even when it is hard to hear. Juliet wants nothing to do with Paris, and the Nurse knows it, but the Nurse makes the recommendation to marry him anyway because she cares about Juliet. She doesn't want to see Juliet in anymore trouble. Furthermore, she helps Juliet see the good in Paris:
Then, since the case so stands as now it doth,
I think it best you married with the County.
O, he's a lovely gentleman!
It is a true and genuine love that the Nurse has for Juliet.