You could host the files on a local HTTP web server running on your PC (or even another android phone).

Connect the phone to a PC, use ADB to install the APK.

Danger Manfred wrote on Today, 14:29:

Now if I could just find a file upload service that still works on the damn phone, my hope is that I could just upload my DOSBox APK there, download it on the phone, then install it from there.

There is a service I use all the time to transfer files when the device only has a web browser. It's free, no registration and is 100% safe to use - it's called your PC.

http://www.rejetto.com/hfs/

Set this up on your Windows PC then drag the files you want transferred to the files window.

Samsung Galaxy S SGH-T959 Android 2.2 Froyo using the built in browser.

Has been very helpful for downloading from my PC with any practically any web browser. My phone has a built in file manager named "Files" but it could be named something else on your phone. I think I tried DOSBOX Turbo on this phone and its performance was sub-par.

P.S. Good luck finding APKs that still work on such an ancient Android version. Please let us know if you were able to get DOSBOX Turbo working and what kind of performance you get.

I've still got an ancient 2.x Android tablet which I still sometimes use and have gotten things to install (It's a weird one - a 7" tablet, but partially thinks it a phone - has a SIM slot and a couple phone related apps)

If you are lucky, you may be able to connect to a PC via USB and access some folders, and "drag" your APK into "Download" or whatever it's called and activate it from there within your "Downloads" app.

Or - old Android sometimes treats the SD card as an extension to main storage, and recognizes certain directories under it, maybe it will recognize a certain directory as an extension to downloads, and you could put the APK there - this will involve some reasearch on the phone to see if/where file system extensions are on the SD.

I've also seen phones which would auto-offer to install .APKs on the SD root or even more often, root of attached USB flash (assuming you phone supports OTG usb).

Or, there might be some app (even browser) where you can manually put in path to file to have it activate.. Depends a lot of the apps and OS implementaion.

-- If you are able to figure out a way to install things, also put on a proper file manager - I've used "ESfileExplorer" on some (It likes to "phone home", but can be blocked)
... And, as someone anal about "not losing stuff" I have backups of almost all the .APKs that I've used over the years, even going back to some very old ones .. I might be able to help you out if you need something old enough to work on 2.3

Btw, DOSBOX Turbo on Android was the main reason I wrote my KEYSUB tool - super tiny key-remap that happens at the BIOS INT 16h level. Remap keys by raw scancodes... only way I could get DosBox on Android with an external keyboard truly usable.

Android phones of that era were not plug-n-play. They required device drivers and an Itunes-alike software to transfer files and only supported media types (Audio and video) could be transferred. As I recall when I first got this phone it came with Android 2.1 Eclair but the upgrade to 2.2 offered not only built in Adobe Flash Player but an optional USB Storage mode that treated the phone as a standard USB storage device.

Turns out even the App Installer is missing from the phone.
How I found out: I used minimal adb and fastboot to push a file manager app to the phone, that even installed somehow.
But then when I wanted to use the file manager to navigate to the .apk and install it, I got an error message that there is no app for that.
Okay, no problem, I'll just push an app installer app next.
Suddenly, nothing gets pushed/installed any more, see attachment.
(ai.apk is an app installer, the filename was horribly long and contained special characters so I renamed it)

Norton Commander wrote on Today, 19:28:

Android phones of that era were not plug-n-play. They required device drivers and an Itunes-alike software to transfer files and only supported media types (Audio and video) could be transferred. As I recall when I first got this phone it came with Android 2.1 Eclair but the upgrade to 2.2 offered not only built in Adobe Flash Player but an optional USB Storage mode that treated the phone as a standard USB storage device.

Hmmm, I think some of your experience was deliberate vendor lockout of features by the phone carrier. Remember at this time they wanted to charge you a couple of bucks per ringtone and that sort of shenanigans. Still happens, some android devices can't do hotspotting because carrier locked it.