If you're only getting BA flights suggested by the Avios.com website, that would suggest that Aer Lingus don't have any/enough seats for the dates and flights you're searching for.

Without knowing what route(s) you're interested in all I can suggest is - search for different dates, further in the future. If you're looking for seats for busy dates in the near future - say, Easter holidays - then it's not surprising that there's nothing available on Aer Lingus any more.

When looking to secure reward seats, it pays to book very early (the seats become available to book about a year in advance) or to be very flexible with what you accept.