Will those clips Frank showed be sufficient to support a tabletop attached only at the ends?
Well...no not really if you want a proper job of it? They can be made to work, but aren't really intended for this application...
Table Top Clips (aka Apron Clips)
are a product steaming from mass production post Victorian Age and the Industrial Revolution. It's a "dumbed down" method of construction that has slowing (like many things in modern woodworking?) seeped into the world of day to day practice of the craft as we find it now. They are meant (mainly) for table designs with aprons and for "mass production" tables manufacture (for the most part) and not higher quality tables. I have used them to repair tables that are already designed with them in place, but I don't design and/or build with them for the most part.
Harvest, Farm, and related "Folk Style" furniture are from a much older (ancient actually) system of building furniture akin to the buildings they often found themselves used in like timber frames...and...built pretty much the same way...with green wood and all wood joinery.
We don't need to explore the "greenwood" traditional side of this for your project since you're already trying to finish the design you have out but we can discuss the many different ways to attach (and/or position?) your top on the supporting framework.
It's going to be rather difficult to really recommend an approach without seeing what you have design and built thus far? Sliding Spline Keys...a single locked trunnell in the center of the table top and then into the trestle frame on both ends...dovetail sliding through tenon with wedges into trestle frame...toggle binding (rare and I'm the only one that does it in this country that I know of?) ...or a simple peg or dovetail key are but a few of the traditional methods that work well for these marvels tables of history!
Post some pictures of the trestle and table top (from underneath as well) and the dimensions, and I might be able to suggest something germane to your needs?