The 175/60 R13 size that Hans mentioned is the theoretically the closest in rolling radius to the 165/60 R13. Theoretically this is just 6mm bigger in radius, but the actual rolling radius and tread width tends to vary from make to make which makes the selection even harder.
To make things harder, the different Midas models have different sized wheel arches, getting larger with each model, so the Mk4 models have more space than the Mk3 Convertible, which is slightly more generous than the Mk3 Coupe, which in turn is larger than the Mk2. Given that information, I would tend to go down slightly on rolling radius for a Mk2 - 175/50 R13 (11mm down on radius) or 165/55 R13 (8mm down on radius). I'm told by my friendly MOT inspector that a 5mm gap must be seen between the tyre and the arch.
I have had more experience with the Mk3 and Mk4 models so can pass this on.:
I have fitted 185/55 R13 tyres (3mm bigger radius but 20mm wider) to both Mk4 models (Cortez and Excelsior) with no problems and also to a Gold convertible, which took a bit of tweaking to clear the back of the arches. However these are now rare as hens teeth. Toyo seem to bring in a couple of shipments each year and they sell out in weeks!
I have seen 165/65 R13s (8mm bigger radius) on several Mk4s and these are fine, but I have also seen two Mk3 convertibles with them fitted that had problems with them touching the top of the arches during cornering. In my view this is much more serious than touching the back of the arch when on full lock - you would only use full lock during slow manoeuvres and the effect is just to rub the tyre on the arch. Whereas, the tyres only touch the arch tops during cornering (at speed) and have the effect of grabbing the tyre, acting as a brake and effectively locking the steering (yikes!
). Of course this may only happen to the particular brands fitted, but I can't recommend the 165/65 R13 for Mk3s or Mk2s.
I have recently fitted a set of 175/60 R13s to a Mk3 Coupe. These touched the front lower lip of the inner arch and the back of the nearside arch. Why the back of the NS arch and not the OS arch too? It turned out that the wheelbase on the NS was around 5mm shorter than on the OS! Further measurements showed this was in the mounting of the front subframe and a 3mm shim washer between the rear subframe mounting and the subframe brought things level (the subframe mounting is inboard of the wheel, so any shimming at the subframe is multiplied at the wheel). Just to improve things further, I also shimmed the spacers behind the ARB a further 3mm, a la Metro turbo. This increases castor slightly, which increases the self centering effect and improving steering feedback, but making the steering slightly heavier. How much heavier is hard to tell as the wider 175 tyre also increases steering load, but in my view the driving experience is improved. Obviously this all moved the wheels forward and it was already touching at the front on full lock. However, the bottom lip at the front of the arch is easier still to deal with as I simply cut it out and moved it forward by half an inch (approx 12mm for those too young to know what an inch looks like), re-laminating it back in its new position.