Can I pay equal amounts of quarterly tax if my income is uneven?

It depends on which safe harbor you are going for. If you are trying for the safe harbor of paying 100% (or 110% for high earners) of last year's tax liability, then yes, you can just pay 1/4 of that amount each quarter and be sure that you won't have a penalty.

If you are trying for the safe harbor of paying 90% of this year's tax liability, there are 2 ways of calculating how much estimated tax you must pay each quarter: 1) pay 1/4 of the safe harbor each quarter, or 2) the Annualized Income method, which considers the income you have made up to each quarter. As for paying 1/4 each quarter, the problem is that you don't know what this year's income will be. If you pay 1/4 of 90% of your estimate of this year's tax liability each quarter, and your estimate turns out to be right, then everything is fine; you have no penalty. But if your estimate is wrong and you unexpectedly get more income in later quarters, then you're screwed -- you would not have met the 1/4 of 90% of this year's tax liability in the first quarter, and you would have a penalty. So if you are going with this year's tax liability, to be safe, you should pay enough for each quarter under the Annualized Income method. That way, you won't have a penalty no matter what changes in income you have in the rest of the year.

(By the way, everything I said above is only if you are trying to meet the safe harbor through estimated taxes instead of through withholding. If you can increase your withholding such that, by the end of the year, the taxes withheld alone (without estimated taxes) reaches either of the safe harbors, you will not have a penalty. This is true no matter how you your withholding is distributed over the year. So you can "fix" insufficient estimated taxes in earlier quarters through increased withholding in later quarters, whereas you cannot fix it through increased estimated taxes in later quarters.)