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Aims. Diffuse interstellar bands (DIBs) measured in stellar spectra contain information on the amount of interstellar (IS) matter that is distributed along the line-of-sight, and similarly to other absorbing species may be used to locate IS clouds. Here we present a new database of 5780.5 and 6283.8 Å DIB measurements. Those two DIBs have the advantage that they are strong and also broad enough to be detectable in cool-star spectra. We also study their correlation with the reddening. Methods. The database is based on high-resolution, high-quality spectra of early-type nearby stars located in the southern hemisphere at an average distance of 300 pc. Equivalent widths of the two DIBs were determined by means of a realistic continuum fitting and synthetic atmospheric transmissions. For all stars that possess a precise measurement of their color excess, we compare the DIBs and the extinction. Results. We find average linear relationships of the DIBS and the color excess based on ≃120 and 130 objects that agree well with those of a previous survey of ≃130 northern hemisphere stars closer than 550 pc. Because our target sky coverage is complementary, this similarity shows that there is no significant spatial dependence of the average relationship in the solar neighborhood within ≃ 600 pc. A noticeably different result is our higher degree of correlation of the two DIBs with the extinction, especially for the 5780 Å DIB. We demonstrate that it is simply due to the lower temperature and intrinsic luminosity of our targets. Using cooler target stars reduces the number of outliers, especially for nearby stars, confirming that the radiation field of UV bright stars has a significant influence on the DIB strength. We illustrate the potential use of 3D maps of the ISM for characterizing the DIB sites. There is some evidence that interstellar cavity boundaries are DIB-deficient, although definite conclusions will have to wait for maps with a higher resolution. Finally, we have used the cleanest data to compute updated DIB shapes.