Create a NON-Clustered index on the filtered column which you are issuing in DELETE statement and see if that fixes the dead locking issue to complete the statement.

It seems other SPID's are trying to process(select / update/ delete) the data in the table which you are trying to delete the data. You can run the profiler to capture deadlockgraph, if you want to see which statements are trying to access the data in that table.