Recommendation for trainer tire 28 x 1 5/8 x 1 3/8 I started with a 700x32c Continental Hometrainer tire.  It seemed to work out OK at first, but in the last few times I've had to switch between my commuter/road tire and the trainer tire, it seems to have become more and more difficult to get the tire even around the rim.  Tonight, I was putting it on, and I have pretty much given up.  There is about a 6-8 inch section that is definitely not seating the bead to the rim, no matter how much I carefully work the whole tire around the rim as I inflate it.  I've checked the inner tube, and it is not twisted or anything.  It seems that the tire is simply small for the size of the rim for which I've gotten 28 x 1 5/8 x 1 3/8 commuter tires.

I'm looking for a recommended trainer tire to get as a replacement.  I've searched via Google and Amazon, and there don't appear to be any direct 28 inch sized tires for trainers.  Any suggestions?

Regards,
Bruce
The rim you have is a 700c (ISO 622) rim. You can use any 700c trainer tire on it (the tires will be labeled as ETRTO __-622 or 700x__ possibly with a "c" somewhere). The tire you commute on is a 700x35/37c tire and the trainer tire you have selected is one correctly sized trainer tire for this wheel. 

It's probably best to refer to the wheel as a 700c wheel, since that will be the terminology most people will be familiar with. Tire sizing is a mess due to different standards, so I suggest you refer to the wheel and tires you need in the forms above. Most people are not familiar with the inches+fractions system of tire sizing (which is not interchangeable with inches+decimals), and it can lead to confusion. The French system (700c) or ISO/ETRTO systems (ISO/ETRTO 622) specifications are much more common (with the tire sizes specified above). 



We don't do product recommendation here, but if you're regularly switching between trainer tires and road tires, you should consider getting a second wheel set which you can mount tires just for training (well, if you're using a trainer, just a rear wheel). This is a decent strategy if you do tire swaps regularly. The wheel doesn't have to be expensive, just compatible with your drive train. 

Also, see our various questions on difficult to mount tires, such as this one. Some tire and rim combos are difficult.