reinstalling Yosemite from recovery mode on 2009 imac

Your mac can of course run El Capitan, you are wrong on that count.

If it is a late 2009 iMac it can upgrade to macOS High Sierra.

You do not need to erase your mac in order to install another OS.

As you have found out it is difficult to reinstall an OS through Apples Recovery Servers.

The certificates for several of Apples OS's expired in October 2019, Apple have been very poor at getting these updated on their Recovery Servers with valid certificates. This may be the problem you are experiencing. 

Try this workaround, we are going to set the time and date on your mac to a date previous to the expiry date of the certificates.

Connect your mac to your router via cable, not WiFi

Boot to your Recovery HD, click on Utilities in the menubar select Terminal.

Make sure WiFi is switched off, it can reset the date back to today.

Enter a new date, for example or just copy and paste

sudo date -u 011421002015

press Return

enter your password

press Return

If Terminal returns an error saying sudo : command not found, then try again without sudo.

Now try downloading the OS.

If this works then when the OS is installed and booted up you can Open System Preferences> Date & Time

and reset the time back to today.

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If the above method does not work then try this instead.

Do you have another mac or can you borrow one. This mac needs to be able to run Yosemite or El Capitan.

Here are the instructions for downloading and creating the Install app for Yosemite, the instructions for

El Capitan are the same so just replace any mention of Yosemite with El Capitan.

Both of these downloads have valid certificates so no need to alter the date.

Click on the links below to access the downloads for the two OS's.

How to upgrade to OS X Yosemite – Apple Support

How to upgrade to OS X El Capitan – Apple Support

Go to Section 4 and click on Download OS X Yosemite.

This downloads InstallMacOSX.dmg to your Downloads folder.

The next section can only be done on a mac that is capable of running Yosemite,

a mac that came preinstalled with an OS later than Yosemite will refuse to do the next bit.

When downloaded open to InstallMacOSX.pkg, double-click on

that and an installation window will open, this does not install Yosemite

but converts the InstallMacOSX.pkg to the Install OS X Yosemite.app which 

you will find in your Applications folder.

(If the installation window asks which disk you want to install to, you must pick 

the disk that you are booted to at the time. Not any internal or external disk that 

you want to eventually install Yosemite on, that is for later.)

reate a bootable USB installer disk using the Install OS X Yosemite.app

in the Applications folder and the createinstallmedia command in the Terminal app. 

Read the instructions here,

How to create a bootable installer for macOS – Apple Support

sudo /Applications/Install\ OS\ X\ Yosemite.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ OS\ X\ Yosemite.app

When you have created the bootable installer plug it directly into the mac.

Restart the mac while pressing and holding the option/ alt key.

In a couple of minutes you will see the Startup Manager, select the USB

and press Return.

The mac will now boot to the USB, you will see a Utilities panel similar

to the one you see when you boot to your Recovery HD.

Click on Install OS X and press Continue.

The installation process should start, follow the prompts.

Either install the OS from the Software Recovery DVDs that came with the computer or you can install Lion, if you have a Lion installer. You can purchase Lion at the Online Apple Store. The cost is $19.99 (as it was before) plus tax.  It's a download. You will get an email containing a redemption code that you then use at the Mac App Store to download Lion. Save a copy of that installer to your Downloads folder because the installer deletes itself at the end of the installation.

OK, then try this:

Internet/Network Recovery of El Capitan or Later on a Clean Disk

     If possible, back up your files before proceeding.

You will need a fast, working Internet connection, preferably, Ethernet. If you must use Wi-Fi, you will be asked to select your network and enter the network password. This procedure will install the current version of macOS that is compatible with your model.

1. Restart the computer. Immediately, at or before the chime, hold down the (Command-Option-R) keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the target drive (out-dented entry w/type and size) from the Device list.
5. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to APFS (SSDs, only if installing Mojave or Catalina ) or Mac OS Extended, (Journaled.)
8. Provide a volume name, usually "Macintosh HD."
9. Click on the Apply button, then click on the Done button when it activates.
10. Quit Disk Utility and return to the Utility Menu.
11. Select Install OS X and click on the Continue button.