I was surprised to see your question, because I thought the dictionary definitions would make the difference clear. Phonology has to do with the sounds of a language, and morphology has to do the forms we use ~ for the tenses of verbs, for instance.
However when I look up morphology in our dictionary, I can understand why you are asking. I see that definition #3 of morphology describes the two words as synonyms. Definition #4 is more helpful. You could look up "morphology" at dictionary.com as well.
If you have still have questions after you have looked at the definitions and the threads relating to these words, you can post them here.
We will ask for specific context, of course, as we always do.
*raises hand and jumps up and down* oo! oo! A first-grade-teacher question!
If you know the difference between an phoneme and a morpheme, it's easier to keep the two separate.
1) Phonemes are the smallest units of sound (English has around 40 of them)
2) Morphemes are the smallest units of meaning
Both Phonology and Morphology study the way words are built, one just deals with it from the sound angle, and the other from the meaning angle.
Thus (via Dictionary.com):
Phonology is the phonological system (the sound bits) of a language or the study of it (the distribution and patterning of speech sounds in a language and of the tacit rules governing pronunciation).
Morphology is the study of the behavior and combination of morphemes (the meaning bits), it studies the patterns of word formation in a particular language, including inflection, derivation, and composition.