There is no evidence that tanning (artificial or natural) can be harmful for breastfeeding moms and their nursing babies. It is also not true that tanning beds will cook you inside if you use them more often. There will be no changes in your milk production too.
If you are having doubts, it is always wise to ask you doctor about tanning while nursing because they can answer all the questions running through your mind right now. There are different kinds of tanning beds, tanning spray and tanning lotions that you can choose from but if you are on a tight budget, suntanning is the best option.