I would really like to have the lyrics for the beginning of the show. thanks.

The lyrics are posted on this site under the heading General Boards at near the top of the page. Click on 'Theme song Lyrics'. The Petticoat Junction lyrics are on page number 3.

Original Seasons before Bea's death..

Come ride the little train that is rolling down the tracks to the junction.
(Petticoat Junction)
Forget about your cares, it is time to relax at the junction.
(Petticoat Junction)

Lotsa curves, you bet. Even more when you get
To the junction, Petticoat Junction.

There's a little hotel called the Shady Rest at the junction.
(Petticoat Junction)
It is run by Kate, come and be her guest at the junction.
(Petticaor Junction)
And that's Uncle Joe, he's a movin' kind of slow at the junction,
Petticoat Junction

After Bea's death, but before the doctor showed up, replace the last two lines with:

It's a real friendly place, come and be our guest at the junction.
(Petticoat Junction)
And that's Uncle Joe, he's a movin' kind of slow at the junction,
Petticoat Junction

And finally, after June Lockhart joins:

It is run by Joe, come and be his guest at the junction.
(Petticoat Junction)
There's our lady M.D., she's a pretty as can be at the junction,
Petticoat Junction

https://www.youtube.com/watch?v=rA6kbSEmNU4

When Bea Benaderet died during season 6 (1968-69), there were about five episodes that featured the first of two lyrical changes in the second verse; however, Wikipedia says the only episode with this particular change was "The Strange Case of Joseph P. Carson" (11/30/1968). But the info according to the video in the above link says the change first started on the episode "Granny, the Baby Expert" (11/2/1968). These lyrical changes in the second verse, bolded, were:
There's a little hotel called the Shady Rest at the junction
(Petticoat Junction)
It's a real friendly place, come and be our guest at the junction
(Petticoat Junction)
And that's Uncle Joe, he's a movin' kind of slow at the junction ...
Petticoat Junction!

Finally, when June Lockhart became part of the permanent cast, the lyric changes in the second verse now were:
There's a little hotel called the Shady Rest at the junction
(Petticoat Junction)
It is run by Joe, come and be his guest at the junction
(Petticoat Junction)
There's our lady M.D., she's as pretty as can be at the junction ...
Petticoat Junction!

~Ben