Can I make doublets with a Genie and a trim saw?
It seems that, according to their website, your Diamond Pacific Genie is able to flatten and polish gemstones using the &quot;right hand wheel&quot; as a platform for, e.g.,

&quot;Lapcraft &quot;No Hole&quot; discs [like this one]. They screw into the right hand wheel adaptor of the Genie, giving you a 6&quot; diameter lap with no bothersome center hole.&quot;


You could also look into exchanging your trim saw blade with a polishing stone, something that is probably dependent on the model and type of connection.
Not to mention that it can be dangerous, as trim saws have different speeds and were designed for different pressure types and lighter attachments.
Try at your own peril :)

There is also a multitude of tutorials on homemade flat lap machines available online.



Although I have no experience with gemstone crafts, and contrary to rebusB's answer, I suspect two not completely flat surfaces will bond perfectly fine and invisibly when using the right bonding: a slow-curing epoxy might work, or G-S Hypo Cement, with which - provided they can be made fluid enough to fill even the smallest visible imperfections - you will be able to join the compounds without a clear visual boundary. As long as the bonding is clear and as thin as possible, I don't think this will be very obvious. You can heat up the glue a little to get rid of air bubbles, as mentioned here.
It's hard to find anything to back up this claim, though, so I suggest trying it out with inexpensive materials (some pieces of glass, perhaps, as this will make any imperfection readily visible).

Lastly, as a friendly reminder: be sure to wear respirator masks when polishing. You don't want metal fume fever, silicosis, or similar illnesses.