I'm no longer sure about my answer. I have been thinking about this over and over in the past few days but cannot reach a definite conclusion for myself. Hence, 'was' instead of 'were' might be the correcter option for the singular. This was also pointed out by @alephzero, here below in the comments.
This is the subjunctive: 'were' is correct and used in either the singular and the plural forms. Hence, in your specific example:
Singular: If I had a daughter who were cute, I would be very happy.
Plural: If I had two daughters who were cute, I would be very happy.
Some native speakers, potentially Americans more than British, might say that 'was' would also be correct. However, the intention of your statement is presumably 100% hypothetical, insinuating that you are never going to have a cute daughter. The subjunctive should be used.
The most famous exemplary sentence of the subjunctive is probably 'If I were you I would...'
I believe that in modern colloquial English, even native speakers sometimes tend to replace 'were' with 'is' or 'was'.