Hi Greg
Thanks for your post. Kettlebells and the TRX are a tremendous compliment to one another and a formidable duo when paired together. I'm sure that your 55 year old machine is looking pretty good these days.
Your question is a very difficult one to answer simply because of the breadth of movements that the TRX is capable of. The core exercises really depend on what the individual is training for specifically and what elements of their strength and mobility are in most need. In essence I actually can't answer your question correctly without vastly understating how you could effectively employ the TRX into your programming.
Now that I've qualified my answer, I'll actually try to give it my best shot. As opposed to core exercises let's look at these as the movements that I think are generally indispensible and we can go from there
1. Suspended Lunge Series (standard, w power, crossing, abducted, with rotations, DB lifts, heavy ball catches & throws)
2. Row Series (low, high, 45 degrees, single arm, hand position variations)
3. Chest Press Series (deep, single leg, single arm)
4. Shoulder Series (low, L, T, W, Y, I)
5. Suspended Core Work (side plank w reach throughs, pendulum swings, atomic pushup matrix, body saw)
OK... so there are my 5 but I feel like I am completely cheating you as there are dozens more that I use regularly and 100s more that you could employ for specific purposes and that doesn't even take into account mobility based exercises.
I'm also expecting an onslaught from the rest of the community as I'm sure I have neglected to put in someone's favourite movement. If this is the case, please chime in for those of you reading who feel slighted.
This is a good place to start from though. Please keep us in the loop as to what sequences you put together as I'm sure everyone will be interested.
Good luck with your training. I hope that this has helped you organize things a little.