Is there any way to find out deleted transport requests logs?

If you have deleted from SAP level. Then you need to check at the OS level in /usr/sap/trans/log directory else you can check for the SLOG and ALOG folder also.

If total request has been deleted then you can also do the transport manually at OS level.

or

If you have simply deleted the the requests from import queue through "Extras-> Delete imported requests" in transaction STMS_IMPORT and have not deleted the logs at OS level, then you can check in "Goto-> Import History" in the same transaction to view the requests. 

Just double click on the request you want and you enter the "Display Object List" screen for the particular request. 
Here you can click on the secong "Spectacles" icon to display the transport steps of the request in each of your SAP system.
Just double click on a step, e.g. 'Import', 'Check Version','Export' etc. to display the log for that particular step.

You can also view the logs from operating system in the directory <TRANSDIR>/log. The logs are named in the format: 
<Source SID><Step ID><Request no>.<Target SID>, where step ID is a single alphabet denoting a particular transport action.                                                                                                       *-- Krishna

Find Request Number 
Find Your Transport Request Number Even If You Forgot

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