Old style drum machine

Creed_Clicks

DRM-16 app. Basic, and turn a few knobs, and away you go

wolsnah

Would something along the lines of a Yamaha RY8 fit the bill? I picked one up cheap a couple of years back just for messing around on. Possibly worth keeping your eye out for one as they're usually not too expensive.

MartinBush

Thanks to everyone for the feedback on this one. Lots of interesting ideas.

I've now sorted something which may or may not work out for me - if it does I will record and post a track on here and see what people make of it.

maltingsaudio

Late to the party but a hacked copy of band in a box would possibly suit the bill depending on your computer sound card 

greejn

Boss DR-3 is one I really like, simple but great sounds, IMHO

marxski

If you mean a real old sounding analog the TT-78 by Cyclonic is a take on a Roland TR68 but no presets you have to program them from scratch. However there is a free/ donationware  plugin call BucketPops which is modelled on things like the Korg Minipops and has organ style cha cha bossa nova organ style presets. If you are after that David Bowie Low, Jean Michelle Jarre type of sound then it does it very well. 

https://www.fullbucket.de/music/bucketpops.html

LordBucketHead

I use this quite often. Just use the presets on the preset button (scroll down to see the full list). Alter the speed to suit. 
https://tinyurl.com/2dubr9x6

Funkfingers

Fingerlabs DM-1 is available for both iPhone and Android devices.

Shedloads of kits. Easy step time programming or simply hit the Randomizer "button" until it spits out something usable.