As a con artist you would probably just lie. But if you were actually interested in making contact relics, and you had access to an existing relic in a church or private collection, you could manufacture them with relative ease. Relics can generally be sorted into three groups, of varying levels of sacredness:

• primary relics, basically bits of saints' bodies, think of your holy foreskins and vials of blood and little finger bones, etc.
• secondary relics, or objects that have come into contact with/been used by the saints, so clothes, shrouds, possessions.
• tertiary relics, or objects that have touched a primary or secondary relic, and are made sacred through contact.

So if you've got an excess of, say rubbish fabric, and you live close to the tomb of a saint - voila. Relic to sell. Or if you happen to know a rich guy who has the desiccated eyeball of St Boring you can press that old ring your Nan gave you before she caught the plague on it, and then make a few quid. Just make sure no one catches you, or the church might get a bit annoyed, and in the medieval period they were less "turn the other cheek" and more "give him a little stab for being a bastard."