The Sky Blues, who sacked Aidy Boothroyd on Monday, went behind when Rodriguez lobbed Keiren Westwood.
Reports have suggested Commons Speaker Betty Boothroyd will announce a change in this situation next month.
The Republic of Ireland Under-21 international played under new U's boss Aidy Boothroyd at Vicarage Road.
Betty Boothroyd, the speaker, fights a sustained rearguard action to preserve the Commons of yore.
Miss Boothroyd also stressed the need for greater parliamentary scrutiny through select committees, questions and adjournment debates.
Boothroyd rejected the idea that the Reading players should have allowed Watford to score following the error.
Former Watford boss Boothroyd, 38, has "declared an interest" in the job but is third favourite at 7-1.
The first woman Speaker, Betty Boothroyd (Labour) was chosen in 1992 (in the first contested election since 1951).
Mrs Boothroyd ruled after the 1997 general election that what she called "associate status" for MPs did not exist.
And following a poor start to last season, Boothroyd left by mutual consent.
King was dismissed for a reckless lunge on the hour - but Aidy Boothroyd's side held on for a draw.
Managerless Coventry, who sacked Aidy Boothroyd a fortnight ago, are 20th in the Championship - just seven points away from danger.
Former Wales captain Gary Speed has been approached by Swansea while ex-Watford boss Aidy Boothroyd and Exeter manager Paul Tisdale have been linked.
He appeared briefly in the first Bond film Dr No in 1962 under his real name Major Boothroyd, played by actor Peter Burton.
Poyet has already held talks with Swansea chairman Huw Jenkins, as has Sheffield United player coach Gary Speed and former Watford manager Aidy Boothroyd.
And Labour peer, ex-Commons speaker Baroness Boothroyd, said the House of Lords "worked" in its current form and there was "little appetite" for reform.
Former Watford boss Aidy Boothroyd is also known to be keeping an interest in the vacancy as Jenkins confirmed the 38-year-old had "declared an interest".
Judge Stokes praised Ms Green's friends Janet Boothroyd and her husband Paul who had investigated the case for two years before it came to court.
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"Form goes out of the window in the play-offs, " said Boothroyd.
Even Betty Boothroyd, the House's unflappable speaker, who announced her retirement this week, has had to chide the government for telling the Commons everything last.
Boothroyd, who took the Hornets into the Premier League for a season in 2006, has been out of work since leaving Vicarage Road last November by mutual consent.
Watford boss Aidy Boothroyd has earned a reputation for motivating his players - and it is clear that installing confidence in his team is one of his fortes.
"He scored a lot of goals and did very well for me and I just thought it was the right time to perhaps bring him, " Boothroyd told BBC Essex.
In Songs of Praise, Michael Buerk also meets Betty Boothroyd, the first woman to be Speaker of the House of Commons, who tells him she relaxes by going paragliding.
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Another Premiership manager who has seen Healy at close quarters is Watford's Aidy Boothroyd, who was on the staff at Leeds when the striker moved to Elland Road from Deepdale.
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Dr Boothroyd said previously it had been thought selecting partners similar to our parents was because our parents are the people from whom we learn what our species looks like.
Superficially, giving those powers to Betty Boothroyd, the current speaker, or her successors as speaker might seem to get around that, since her office is by tradition a non-partisan one.
Former Wales captain Gary Speed, ex-Watford manager Aidy Boothroyd and Exeter City's back-to-back promotion winning boss Paul Tidsdale have been linked with the Swans job that Martinez helped make so appealing.
Miss Boothroyd, or "our Betty" as Labour's Peter Snape described her, also broke a few traditions herself by using her statement to urge MPs and ministers, once again, not to downgrade Parliament.
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