I'm not sure what kind of trellis you are constructing, but I have used clothesline to build a cucumber trellis. I used the plastic type clothesline since it is UV and weather resistant. The coated wire type should work well too as long as you aren't putting much weight on it. This type of clothesline was around $9.00 for 100 foot roll at Home Depot.

I have added a link to my cucumber trellis so that it give you a visual of what mine looks like.

I hope this helps you!