In reply to kingborris:
The Alpkit Jackal internal diameter is given in the specs sheet as 99mm the Jetboil Coffee Press is given as 117 mm dia for MiniMo / Sumo or 100 mm for the Flash, Flash Lite, MicroMo and Zip.
Based on that I think the smaller diameter jetboil might be a nice tight fit, however when faced with a similar problem I went down to the local Wilko's and looked through the cafetiere's and brought one (£5ish) and use the press out of that in mine.