A pic of the knife would be very helpful. OR, at least a specific description of the make & model. Assuming side-to-side play, and NOT up-down:
If it's a solid metal-bolstered knife (brass, nickel or stainless) with a pinned pivot (not screwed), a very gentle, careful squeeze in a vise might snug it up. Wrap the bolster in leather or heavy fabric, sandwich it between a couple pieces of wood in the vise, then VERY GENTLY snug the vise down on it. A tiny squeeze at a time, re-check the play frequently, so as not to overdo it. It's very easy to make it too tight, if you're overly aggressive with it.
This actually works well with un-bolstered knives too (such as Delrin/wood-handled sodbusters). It's an especially common fix for these, as they're known for loosening up. There are some plastic/nylon-handled lockbacks out there, with peened/riveted pins for the pivot (such as the old Bucklite series, or some older Spydercos, with FRN handles). I don't know if this technique would work well with those.