Nope, not another what should I use, but what I did use and was extremely pleased.
Just sold my "Gambler 4 string, and before I did, I changed the machine heads to better quality and more user friendly, and wasn't happy with the tuning either, I had originally used the EADG wound strings to achieve GDGd, didn't like it.
Here's what I used a set of Martin Acoustic Custom Light strings 80/20 bronze, I used the DGBE strings in the pack, but being custom light strings they were more like the middle 4 on most with the exception of the high E.
The string gauge I used was .032, .023, .015, .011. 2 wound, 2 unwound and tuned to GDGb, all I can say is WOW, woke up this guitar big time, sounded sweet, intonation was easy, not too buttery, sounded good both acoustically and electric piezo pickup(50mm 1 disc) It was a 25.5 scale.
I use the 4 inside strings of a 6 string set 10-46 gauge(A-36/D-26/G-17/B-13) and tune G/D/G/B. If I want to get some different sounds, I can tune A/D/G/B for some good Rock A power chords and A blues(ZZ Top, Zepplin, Hendrix, Aerosmith) or tune it G/D/F/B for G7 Blues tuning. 3 different tunings with little adjustment - very versatile.
Some use the 4 highest/lightest strings(D-26/G-17/B-13/E-10) to use a D/F/A/D or D/G/A/D(drop the 3rd for a 4th) or D/A/C/D For D7. Or drop tune to open C - C/F/G/E.
I think your D/G/Db/A is more of a D4 minor. I'm rusty on my chord theory.
The title said DGDb was a typo, dyslexia, sorry, all fixed.
Ah, that makes a difference. ;) A 1-5-1-2 tuning works.
I have one I did the same with. I just don't really like the 1-5-1-3 tuning too much. That last string always sounds too bright.