Here is a grape grafting technique I ran across today. Air layering is generally very easy to do, either using plastic bottles, or burying part of the vine. ....The vine, however, does not unite as readily as pear and apple would when grafted. To ensure success, grape vines must be grafted under ground, which makes the operation a difficult and disagreeable one. It will therefore hardly become a general practice; but, for the purposes above named, is of sufficient importance, to make it desirable that every vineyardist should be able to perform it. Generally the best time to successfully graft in the Midwest is in about the middle of March, in the following manner: Dig away the ground around the vine you wish to graft, until you come to a smooth place to insert your scion; then cut off the vine with a sharp knife, and insert one or two scions, as in common cleft-grafting, taking care to cut the wedge on the scion very thin, with shoulders on both sides, cutting your scion with two eyes to better insure success.
Great care must be taken to insert the scion properly, as the inner bark or liber of the vine is very thin, and the success of the operation depends upon a perfect junction of the stock and scion. If the vine is strong enough to hold the scion firmly, no further bandage is necessary; if not, it should be wound firmly and evenly with bass bark. Then press the soil firmly on the cut, and fill up the hole with well-pulverized earth, to the top of the scion. Examine the stock from time to time, and remove all wild shoots and suckers, which it may throw up, as they will rob the graft of nourishment and enfeeble it. Source NDSU plant propagation.