I was told by a priest that sexual intercourse between unmarried persons is acceptable so long as it reflects a relationship of love. Lots of perople seem to believe this, but is it true?

The only "relationship of love" that makes sexual intercourse acceptable is a marital one. The priest who told you otherwise wasn't presenting Catholic teaching on the subject, but his own (erroneous) opinion.

In its Declaration on Certain Problems of Sexual Ethics, the Vatican Congregation for the Doctrine of the Faith reaffirmed traditional Catholic teaching on the subject of sexual relations outside marriage:

"Nowadays many claim the right to sexual intercourse before marriage, at least for those who have a firm intention of marrying and whose love for one another, conjugal as it were, is deemed to demand this as a natural outcome...This opinion is contrary to Christian teaching which asserts that sexual intercourse may take place only within marriage (no.7)"