In the past, people worked out how to match Tamiya paints to LEGO colours, but it requires a tool that no longer exists on the internet. I am currently trying to find either a way of matching paint to LEGO in general or a paint that matches Dark Bluish Grey
You can get paint colour-matched, either automotive (good for metal and some plastics) or domestic (for walls, wood, possibly also metal). It's not cheap though.
Look for "paint match service", and find one where you actually take in a sample. The sheen won't be a perfect match, though there may be a choice, and lighting can bring out differences (e.g. if you're painting a large background to match a display.
Alternatively, and quite possibly close enough, there are places with a very wide range of stock colours of car paint. You may have to buy the two or three closest and test on your chosen substrate or something similar; this could still be cheaper, and may be more appropriate given that your mention of Tamiya paints implies small quantities
There are a few specialist paint suppliers that claim to offer the full range of Pantone® colours, for example in the UK you get a 30ml sample pot of 431-C for about £5 from Riolet Custom Aerosols.
Note that there appears to be some disagreement over which Pantone colour matches which LEGO colour, and indeed some disagreement over which hex colour matches which LEGO or Pantone colour...
So somewhere between Pantone 431 and Pantone Cool Grey 10 is probably LEGO Dark Blueish Grey.