Glad to know that you own a well-maintained Maruti 800 1995. However, I am sorry to tell you that finding decent Bias-ply ( Non-radial) tyres in size 5.65-12" would be a very tough thing. This is because almost all passenger car tyres these days are radials.
And even I would suggest you to use radial tyres as they offer better handling and performance.
For your 800,you could look at Goodyear GPS2 tyre. It is a decent option to begin with.
A better option would be Falken Sincera SN835.
And in case you want exceptionally good tyres then go for Michelin Energy XM2.
Our database does not recommend an upsize to 13" rims. Tyres in these sizes would make handling stiffer and the the ride comfort would be highly compromised.
We suggest you stick to the stock tyre size of 145/70 R12. If you want wider tyres then at the most you can upsize to 155/70 R12 tyres.
Since the running of your car is very little it's better to go for soft compound tyre. The tyre rubber tends to harden over time as it loses the oils in it. Your major concern is degradation due to time rather than tread wear. Therefore, you can consider tyres like Falken Sincera SN835 and Michelin Energy XM2. Also read this article- http://tyres.cardekho.com/news/should-you-replace-your-tyres-even-if-the-threads-arent-worn-out/
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