Can anyone give this south Texas girl some advice on whether it would be too cold to rent a convertible for a trip along the coast and then Yosemite in late May, early June?

A convertible at that time is an exellent idea. The rains will be over and temperatures will be warming up. Along the coast, you will probably encounter some coastal fog and in Yosemite mornings and evennings may be chilly, but overall the weather should be really nice.

I don't think it'd be too cold. I've been to Yosemite in late May and found the weather to be quite pleasant, though it can change quickly.
The only comment I have on the convertible is that it may not be the best car to handle the hilly roads leading into and out of Yosemite. I rented a convertible when I went there and swore I would never do that again. I don't mind perilous roads, but I found in a convertible - being so low to the ground- I couldn't judge the road as well as I could in a SUV.
But that's me. Have fun.

Had the top down in the Miata yesterday......ahhhhh.

I have to tell you, we've driven that Miata almost everywhere. Even up to Big Bear to go skiing. I actually prefer it to taking the Expedition since it handles much better than the big blue barge.

Anyway, Coast Highway is a blast in a convertible. Go for it.

May can be bug time in the Sierra, small gray flying beetles, flying large ants on occasion, large flies. Probably nothing compared to Texas, but you could find some passengers after a hike to a Yosemite waterfall.