It's only suicide if you haven't built up an army in Italy beforehand. If that is so, you should probably start doing that as soon as possible. In fact, get 3 or 4 armies.

How does the armies you have in Italy affect what the senate tells you to do?

And I do have an army in a fort sitting right next to the rome capua border, a 4 star general, mercenary elephants, 7 urbans, 5 praetorian cavalry, 3 hoplites, 3 bastarnae

If your army is that strong, then you must be deep in the game.

Suicide requests are the game's way of saying it is time to ignite the civil war. You basically have only two options.

1) You ignore it (refuse) and the Senate casts you out, declares war, and all Roman alliances end. The civil war is on.

or

2) You agree, your faction leader dies, and the Senate asks you again next turn. Or, being the Senate, it takes the body of your dead faction leader, casts you out, declares war, and all Roman alliances end. The civil war is on anyway. Though mostly they accept the sacrifice. This can go on until you run out of family members and lose the game.

In my learned opinion, option 1 is best. Take your army and cut their throats, storm their cities, and generally ruin their lives for giving you such a smelly end of the short stick.

So there is no known way to ignore the message and move on without consequences?

To answer that simply, no. Your best bet is to prepare your armies and get ready for the long haul.

the best way is to choose the start of the civil war yourself

i usually do that as soon as its possible because then the main forces of the other roman civs are far away on expansion and italy will be yours

Crusiminator is right. You can start the civil war yourself without having a suicide demand from the senate only if your popularity with the people increases fast enough. But this takes some clever "political maneuvering".

The AI will tell you to start the civil war because you are popular with the people enough to take power for yourself in Rome. When this message appears, STOP expanding and bring your armies back to take Rome. If you continue to expand, your people popularity will increase too much and the senate will soon demand your faction leader's suicide.

At the same time, delay the senate's displeasure by complying with their missions if reasonable, while building up your forces near Rome for the civil war. The result of the political maneuvering is that your senate popularity will hover at average (because of your people popularity), yet your people popularity is high enough to start the civil war without incurring a suicide demand.

Btw, quirky things can happen sometimes on the senate missions screen if you do not attack the senate first in the civil war. Here's what I saw on mine:

Mission: Attack outlaw faction
Time remaining: Minus 2 turns
Target: Scipii
Penalty: You will be outlawed

But I've already destroyed the Scipii and am already outlawed by the senate! Duh! Anyway, I taught those old bench warmers a lesson.