you just need flatwound strings.
i recommend:
Thomastik JF344 or JF364 Flatwound Long Scale 4-String Jazz Bass
Strings
Rotosound RS77LD Jazz Bass Strings
Ernie Ball 2810 Flatwound Bass Strings Set

Upright sound might want Tapewounds more than Flats.

I've found the Thomastiks wonderful but not all that uprighty, especially if you dig in. D'Addario Chromes were closer, but still bright-ish. No experience with Rotos or Ernies; any experiences out there for uprighty-ness on them compared to TI JFs or D'Add. Chromes?

It's more than the strings though. Fretting hand & palm muting help. Try playing some lines with the edge of your plucking palm ready to mute the strings & pluck with your thumb; brief little notes thumping & burping along in a cool little walking line.

Try messing around with the EQing as well.

There are not strings made specifically for fretless and what you use is up to your preference. I personally don't like flat or tape wounds on fretless preferring a round wound for feel and sound. If you are worried about fingerboard wear you can try a coated set.

OP wants an upright-y sound. I'm with rounds on fretless too, but I don't find them very upright-sounding.

I've tried tape and flat wound strings but I'm with Brad on this,
round wound strings feel and sound better to me. I'm using a MIM J
bass so I don't really care about the minor fretboard wear.
Mark

I have tried the half rounds and found them a good middle ground between flats (don't like) and rounds (neck wear)

Gumby

i use GHS customs.theyre black tapewound strings. the tapewound kinda look like there thinly wrapped in black plastic. they run about 50-60 bucks a set. you can specially order them from GHS. and yes they do have a lower end tone than a regular bass string.

dont use roundwounds unless u want a tore up frettless board. dosent matter even if it is epoxy coated. round wounds WILL tear grooves in a fretless neck or chip the epoxy reguardless of fretboard wood type etc.

RotoSound RS 88LD TruBass

+1!!

If you wish for an upright-ish sound, then flats or tapes are the way to go. They will have less sustain and more attack and sound somewhat like...an upright.

Some good flats (I've tried all of these):
GHS Precision Flats
D'Addario Chromes
Thomastic-Infield Jazz Flats
Labella Tapewounds
Fender Flats (For Higher Tension)

Doug

AH HA! You're the one I should pester with this!!

Douglas, can I get your opinion on the tonalities of those strings? My experience has been limited to the TI & Chromes. Thanks.

David;

Check you PM box on this one.

Doug

Thanks Doug!!

1st read shows it very informative. Planning many future reads.