There are only two rear tyres currently available that will reliably stay up on the seat on a TY175 rear rim at trials riding pressure
The IRC TUBE TYPE rear tyre is the best for trials competition use. It is current technology compound and carcass design, works very well and are easy to get.
The only other rear TUBE TYPE competition tyre currently avaliable is made by Michelin but is not as good in competition but probably fine for trail riding. Michelin used to make a tube-type version of their fabulous X11 competition rear tyre but they stopped making them a few years ago.
There are lots of TUBELESS rear trials tyres available but they are made for TUBELESS rims which have a different cross-section bead seat that matches the different bead shape of the TUBELESS tyre.
Modern Michelin, IRC and Dunlop fronts are all good for the front end. Beware of anyone trying to sell you a TUBELESS front tyre. All modern trials bikes have TUBE TYPE front rims and so all recently-made front tyres are TUBE TYPE. There was a period in the late 1980s early 1990s when front TUBELESS tyres were standard (it didn't last long) and some tyre sellers still have some of those TUBELESS fronts. Not only will they be rock-hard, but they won't stay up on the bead seat on a TY175 rim, or a modern front rim.
Sorry if I seem like I am banging on about the tyres but being sold the wrong type of tyre for a twinshock bike is a common problem. I am super-careful to specify exactly what I want when buying tyres and still have had to get the local shop to send them back to the distributor (who have sent something different).