Can coconut oil, cranberry grape juice help relieve constipation?

Not ideal. More fibre in the diet plus regular exercise would be the answer. However if you consume enough oil of any kind, you will likely end up with diarrhea. Cranberry grape juice will add a lot of sugar to your diet without helping your bowel.
Yes. Oils and juices can improve and relieve constipation. You should adjust your diet if the constipation is chronic by adding more vegetables and fruits. Sometimes you will need laxatives or stool softeners on an occasional basis. They are available in the pharmacy.