Browser that works for OS 10.6.8 macbook pro (2.26 GHz Intel Core 2 Duo / 2 GB 1067 MHz DDR8?

Safari is updated with OS X / macOS.

With a Mac running a version nearly a dozen back, your OS X and macOS upgrade options will be somewhat limited.

Please post the MacBook Pro year.

This model year info is available from 🍎 > About This Mac.

Intel Core 2 was used in various models in that era.

This might be a MacBook Pro mid 2009, which tops out at OS X 10.11, which is itself old, and you’ll have to manually update some certificates to get much connectivity with Safari.

Here is how to get older mOS X and macOS versions, and you’ll want to go as recent as your MacBook Pro supports:

… How to get old versions of macOS - Apple Support

Here’s how to get an old version of Mozilla Firefox, once you get to OS X 10.9, 10.10, or 10.11:

… https://support.mozilla.org/en-US/kb/how-download-and-install-firefox-mac

You can download iCab v5.2 which supports macOS 10.6 - 10.9. Do this before you take your newer Mac in for repair, and then transfer iCab to a USB Stick and use that source to install it on your 10.6.* Mac.

It is good that you found an alternative Mac and the use of Firefox.

The iCab version compatible with Snow Leopard would very likely be using Internet security protocols that are now long outdated and current when Snow Leopard was still supported by Apple. Thus, websites that take security seriously have now advanced to current versions of those protocols. That can result in site access issues.