Hmm, but unless you know the bank's formula for calculating a credit limit, this would be a big guessing game. You have little idea what credit limit the bank would give based on your real income or on your fake income. If you're hoping for a credit limit of, say, $3,000, how do you know that that isn't what the bank would give based on your real income, and by understating your income they'll give you only $1,000, which you'd consider too small? Or based on your real income they'd give you $20,000 and on your understated income they give you $10,000, which is still more than you want?
Far simpler, I'd think, would be to call the bank and ask what credit limit they'd give you, and if the number they give is too high, ask for a lower limit.
I wonder why you're worried about too high a limit. Reasons that occur to me are, 1. you're worried that some authorized user on the card, a spouse or child or whatever, may run up too many charges, or 2. you're worried that you don't have the self control and you yourself will run up too many charges.
Generally having a large credit limit is good for your credit score, because an important factor in your score is what percentage of your available credit that you're using. I recently applied for 3 new credit cards within a few months to take advantage of special offers (50,000 bonus miles on an airline card, etc). I was a little worried that getting several cards in such a short period would hurt my credit rating, but in fact it went up. Part of the formula is the percentage of available credit that you're using. By getting a bunch of new credit while having the same total debt, my utilization percent went down so my score went up. (And just by the way, one of the airline cards gave me a credit limit of $30,000! Like wow, do they really think that if I ran up $30,000 on a credit card that I could ever pay it back? I wouldn't lend me that much money!)