mulch.

Until mulch decomposes sufficiently, having it be thick will help minimize germinating seeds. Mulch is either always turning into soil, or it is collecting windblown soil so will always eventually become a place for seeds to germinate. I presume you are against using periodic pre and/or post-germination herbicidal treatments ...(?)

An established groundcover that is dense will do a pretty good job at discouraging germinating weed seeds. However, one must monitor it well during the establishment period, and occasionally thereafter to make sure that weeds are kept out of the bed. A pre-emergent herbicide can help. Any groundcover must be selected to be happy with the conditions that exist in the bed.

Thanks Yardvaark...the area is mulched, but obviously not thick enough. I have used chemicals to fight the bermuda and nutgrass which has crept in from his side, but generally I avoid chemicals to control weeds spread by seed. There is an old oak in the area that was stressed during our last hurricane season, so I have been careful about chemicals within its dripline.

I have not tried a pre-emergent (other than corn meal). Is there one you would recommend?

I am in zone 5, but have a similar problem with weed seeds from the road blown in by cars passing by. I have grass there and watch for weeds growing, then spray with a herbicide very carefully as spot treatment, because I have dwarf conifers growing nearby.
Groundcovers I noticed will become weeds after a while, trying to take over the landscape.

Thanks berndnyz5 for responding. Sod was my first thought, and I will probably end up with that. First, I think I will apply cornmeall, lay down damp newspaper, then mulch the heck out of the area. If that doesn't work, I will try a sod strip 5-8 feet along the property boundary. Just the strip would be sodded, the rest of the area I am keeping just mulch because of the oak.

Time out! Let's take a minute to untangle a matter which is confusing to many.

1. Plain cornmeal is used as an organic fungicide to control certain plant fungus problems such as Brown Patch, Southern Blight. It is not a natural pre-emergent weed killer. Nor should it be used as such. It also is a minimal fertilizer.

2. However, CORN GLUTEN MEAL, a by-product of corn processing, has proven to be a useful organic pre-emergent weed killer. Not 100% perfect but the best we have to date for the organic gardener. Much has been written about these two types of corn products here on GW over the years on the Organic Forum. A bit of searching should yield some interesting reading.

Many in the deep south are faced with frustrating weed problems and the shade cast by large live oaks. A common solution is to plant Asiatic jasmine (Trachelospermum asiaticum) in the area as a ground cover. This is an aggressive grower, requiring few plants which is then controlled with a weed eater keeping all trimmed low and tidy. Even though weeds sprout through it and tree debris falls into it, none of this is noticed due to the thick growth of the jasmine if it is well maintained as needed. An old southern gardening trick worth considering.

Thanks nandina for clearing up the corn meal vs gluten issue. My mistake, I noted corn meal, but I actually use cracked corn. Not the same as corn gluten I know (I haven't been able to find gluten in my area), but I have found that it does seem to suppress dandelion and other weeds from sprouting in my grass.

I do have some asiatic jasmine growing in another bed, but I thought it would never be able to compete with these weeds without alot of mulch and pulling until it got established. Thank you for the tip, it too was my backup and I do prefer it over sod.