How can I replace stock download manager that Google Play uses? Yesterday I upgraded my rooted LG Optimus One (P500) running v20g 2.3.3 to CM10 (unofficial) 4.1.1 through this post.

Since the new ROM is unofficial and is in alpha/beta stage there are few known problems. I am able to live up with those problems just to enjoy the new Jelly Bean.  However one undocumented problem about download manager was discovered yesterday, which proved to me nasty.

When I attempt to install any app from Google Play Store, a progress bar appears saying "Downloading..." and the numerical progress indicator 'x/y Kb done' does not come up. At first I thought it should be problem with my WiFi, but other application seems to access Internet correctly.  In concurrence to this behavior, the LEDs in my WiFi modem does not blink, which it usually does when there is a WiFi activity.  Even small apps in the order of 150 Kb takes long time and eventually ends with error.  However, I accidentally noticed that a combination of simultaneous downloads of more than one app, cancelling and starting again etc, made FEW of the downloads to actually progress while other still linger.  So, it is clear that the download manager that Google Play Store relies on is trouble some in my case.

My question is how can I replace that download manager? Installing other download manager does not help as Google Play still uses the troublesome native one only.

Any ideas on how I can use some other download manager for Google Play or to mend the troublesome one?

BTW, I had tried: Turbo Download Manager, Download Manager for Android. They do not detect the download when i press "install" button in Google Play Store for an app. Trying other download manager is still a big pain as I have to download APK from other sites and transfer to my SD card to install.
While you intend to replace the stock download manager, but keep access to Google Play Store, since it's your trusted market, before that, you should try to find the reason as to why are you having troubles downloading apps:

Troubleshooting Download Issues


Is the device supported by Google Play Store?

You can confirm this from the Supported Devices List last updated 2012/06/29
Common quick checks:


Restart your phone, then try downloading the app again.
Confirm there is connectivity to either wireless or cellular networks on your device. 

If behind a firewall, ensure that TCP and UDP 5228 ports aren’t blocked (they are required for Google Play).
Clear cache and data of both the Google Play Store app and the Download manager:


Visit Menu > Settings > Applications > Manage applications;
Tab over to "All";
Select the Google Play Store app, and then tap "Clear data" and "Clear cache";
Select Download manager and tap "Clear data" and "Clear cache".



Aditional information for troubleshooting can be found at Google Play: Troubleshoot an issue.



Alternatives



Other App discovery Method

Appbrain, an app discovery service that as per your request still uses Google Play Store as the source for the downloads provide.

It features a great instant download tool (AppBrain App Market), a nice search function, a very clear interface and you can sign-in with your Google account.

One side note: This app still downloads via the stock download manager.



Alternative Markets

Alternative markets have their own download manager. They may be a solution, provided the issue does not lie with your current unofficial ROM:


Amazon Appstore for Android

While an alternative market, I've received a notice from the website stating:


  The Amazon Appstore is only available to customers located in the United States.

GetJar

Launched in 2004, it grows every day, counts 600.000+ apps, and 450.000+ registered developers. As an independent app store, not tied to any particular handset or carrier, it comes as an alternative solution for you.
AndroidPIT

AndroidPIT is a Web 2.0 network and Android blog. Was created to bring together Android experts, enthusiasts and developers. Apps are tested, at least one every day and reviews are published to help users on their decisions.
SlideME

Founded back in 2008, SlideME provides a 'Managed App-Store Service' and builds solutions as per market requirements.