From http://wdtprs.com/blog/

QUAERITUR: Can a deacon baptize with the older Rituale Romanum?

Want a traditional baptism with the Roman Rite?

Have a deacon but not a priest?

From a deacon reader:

I [...] was recently ordained to the transitional diaconate, asked me whether church law allows him to perform a Baptism using the Extraordinary Form. He will be ordained to the priesthood in June. Can deacons baptize using the Extraordinary Form? And in fact, did deacons baptize at all before VII, or was this never done?

My old pastor, the late Msgr. Richard Schuler, used to tell a story about the furor and cross looks he kicked up when he asked as a transitional deacon to baptize a relative in his home parish.  He did it, but it was a very dicey thing to do.  The old pastor didn’t like the idea at all, but grudgingly conceded.

The point is this:

In the old days, the deacon was the extraordinary minister of solemn baptism.   He had to have permission from the local ordinary or the local pastor to do it.

Therefore, the pastor of the parish can let you, as a deacon, baptize in the newer form or the older form.

I'd like to add that St. Philip, one of the Seven Deacons, baptized the Ethiopian eunuch (Acts 8:38) by the power and permission of the Holy Spirit!