In fact they both prayed, according to the Talmudic interpretation (Yevamot 64a) of the word l’nochach (Gen. 25:21). The Torah says Isaac prayed l’nochach ishto, which literally means “facing his wife”.
One possible translation is that he prayed concerning his wife, beseeching God to give them issue. But the rabbis are certain that they both prayed, Isaac in one corner of the tent and Rebekah in the other.
This rabbinic interpretation may be construed in two ways, both narrowly and also broadly. Narrowly in the sense that the lack of children was distressing to them both, and they were both desperately anxious to become parents.
The broader interpretation tells us something important about the path to marital happiness.
It shows that on the really important things in life, both spouses must share the same feelings, the same wishes, the same principles, the same priorities. On smaller things there is room for disagreement, dialogue, and compromise, but on the big issues they must be agreed.
This is one of the reasons that Judaism is opposed to mixed marriage. It says that when there is basic religious and cultural agreement between the parties, the two of them work together and their marriage is strengthened.
Everybody knows cases where a mixed marriage has lasted, but exceptions to the rule only prove the value of the rule itself.