Is there a term that describes the joy you get from something that you consistently love?

The nearest I can suggest is familiarity. The word is almost what you specify, although perhaps lacks strong enough overtones of contented love.

Familiarity = easy to recognize because previously experienced: familiar sights: a familiar face: I’m not familiar with current research in the field.

familiar adjective (INFORMAL)

informal or friendly, esp. more than is expected: Her familiar tone makes her writing more effective.

Cambridge dictionary

The same source gives us familiarity = a good knowledge of something, or the fact that you know it so well

Something close to that could be contentment

Contentment is an emotional state of satisfaction that can be seen as a mental state, maybe drawn from being at ease in one's situation, body and mind.

The article on ataraxia might also give you some further ideas.

I would think that one would feel warmhearted at the sight of the person oneloves. I think in a less formal register, cosy or comfy (comfortable) might cover your meaning, because they retain the connotation of intimacy with someone.

I reckon satisfaction fits well enough. joy naturally accompanies satisfaction— A commonplace word for something that is often hard to come by.

If this answer sounds a trifle commonplace and you want a fancy word that captures this feeling (which comes when you hear that favourite song of yours), I suggest this beautiful word— je ne sais quoi

something (such as an appealing quality) that cannot be adequately described or expressed

a young actress who has a certain je ne sais quoi.

[Merriam-Webster]

Your word might be flow.

In positive psychology, a flow state, also known colloquially as being in the zone, is the mental state in which a person performing some activity is fully immersed in a feeling of energized focus, full involvement, and enjoyment in the process of the activity.
— Flow (psychology) - Wikipedia