Who is getting married before the justice of the peace? Two Catholics? A Catholic and a person of another religion? Two non-Catholics? Are both of them free to marry? Why are they being married in a civil ceremony rather than a Catholic or religious ceremony?
All of those things could be relevant. If it is a case of a mixed marriage, a dispensation from the Catholic form (before a priest and two witnesses) is possible for sufficient reason, presuming both parties are free to marry. For example, if one of the parties is closely related to a minister, a Catholic wedding might cause family alienation.
But I suspect you have a different kind of case in mind—when a Catholic or Catholics who are not free to marry are involved. Or perhaps for some reason a Catholic is marrying outside the Church without a dispensation.
In such a case the bishop cannot authorize a priest to offer prayers and blessings. I’m sure you can see the likelihood of grave scandal in such cases.
I have heard of some particular cases where a priest decided that his presence at a civil ceremony or one in another religion would give no scandal—it would not be taken for approval or indifference. But
I find it difficult to see how a priest could offer a prayer or blessing without appearing to approve of what the couple are doing and thus create scandal and dismay for many Catholics.