What's the best way to grill veggies like zucchini and red pepper on the grill, if you don't have aluminum foil or a basket type thing?

Agree with directly on the grill.
But would also like to add a small hack; cooling/baking rack (if you have one). Works like a charm. Just oil it well with towel/paper towels or cooking spray.

Don't slice them at all, just put them on the grill whole

i saw this somewhere!!! and tried it last night, shave lengthwise ribbons, thin 1/8". Toss in oil, season, fold r
them like ribbon candy, skewer, adding cherry tomato in between ribbons, get it? looks great

We grill them straight on as well - I slice them thicker than the openings between the grates so they don't fall through, and with veggies such as asparagus I set them crossways and roll rather than flip them while they cook.

How about using skewers?

If you have sliced the vegetables lengthwise, it is easy to oil them, and then place them directly on the grill. Use tongs to turn them.